Overview of sequences related to Boolean functions

Studies of Boolean functions

This page will be a collection of all integer sequences that appear in the project Studies of Boolean functions.
They appear in the following articles: Integer sequences related to Boolean functions, Seal (discrete mathematics), Gender of Boolean functions

Templates: general, seal

Boolean functions
all dense ♂−♀ self-
reverse
self-
dual
sequences a Grass
GrassDrop
Lotus
LotusDrop
HalfCrocus
HalfCrocusDrop
Primula
PrimulaDrop
Hyacinth
HyacinthDrop
~Grass
~GrassDrop
~Grass
~GrassDrop
triangles a, s ExOlive
ExOliveDrop
a, d TurnedExOlive
TurnedExOliveDrop
a, v Willow
WillowDrop
HalfCedar
HalfCedarDrop
Robinia
RobiniaDrop
Hickory
HickoryDrop
Chestnut
ChestnutDrop
Chinkapin
ChinkapinDrop
a, g TurnedWillow
TurnedWillowDrop
families
all dense ♂−♀ self-
reverse
self-
dual
blunt sharp closed unclosed
sequences a Thyme
ThymeDrop
NonSage
NonSageDrop
Sage
SageDrop
NonDubSage
NonDubSageDrop
DubSage
DubSageDrop
triangles a, s Olive
OliveDrop
a, d
a, v
a, g


sequences
name OEIS entries
Aloe A051502 2, 1, 2, 23, 3904, 134156284, 288230371925149328
NonSage A000133 1, 2, 5, 30, 2288, 67172352, 144115192303714304
NonSageDrop 1, 1, 3, 25, 2258, 67170064, 144115192236541952
Clove 1, 4, 22, 1264, 33617920, 72057598265786368
CloveDrop 1, 3, 18, 1242, 33616656, 72057598232168448
Crocus 2, 6, 26, 318, 66674, 4295297718, 18446744099480343818
CrocusDrop 2, 4, 20, 292, 66356, 4295231044, 18446744095185046100
HalfCrocus A246418 1, 3, 13, 159, 33337, 2147648859, 9223372049740171909
HalfCrocusDrop 1, 2, 10, 146, 33178, 2147615522, 9223372047592523050
Dandelion 1, 3, 30, 4080, 134215680, 288230376084602880
DandelionDrop 1, 2, 27, 4050, 134211600, 288230375950387200
factors in DandelionDrop 1, 2, 9, 270, 526320, 4398113617920
Grass A001146 2, 4, 16, 256, 65536, 4294967296, 18446744073709551616
GrassDrop ~A111403 2, 2, 12, 240, 65280, 4294901760, 18446744069414584320
HalfGrass A058891 1, 2, 8, 128, 32768, 2147483648, 9223372036854775808
HalfGrassDrop 1, 1, 6, 120, 32640, 2147450880, 9223372034707292160
SmallGrass A051179 1, 3, 15, 255, 65535, 4294967295, 18446744073709551615
SmallGrassDrop ~A111403 1, 2, 12, 240, 65280, 4294901760, 18446744069414584320
Hyacinth 0, 2, 10, 62, 1138, 330422, 25770792202, 129127208606163477614
HyacinthDrop 0, 2, 8, 52, 1076, 329284, 25770461780, 129127208580392685412
HalfHyacinth A059301 0, 1, 5, 31, 569, 165211, 12885396101, 64563604303081738807
HalfHyacinthDrop 0, 2, 4, 26, 538, 164642, 12885230890, 64563604290196342706
ExAloe 2, 2, 8, 184, 62464, 4293001088, 18446743803209556992
ExAloeDrop 2, 0, 6, 176, 62280, 4292938624, 18446743798916555904
SmallExAloe A305737 1, 2, 8, 184, 62464, 4293001088, 18446743803209556992
SmallExAloeDrop 1, 1, 6, 176, 62280, 4292938624, 18446743798916555904
Lotus A000371 2, 2, 10, 218, 64594, 4294642034, 18446744047940725978
LotusDrop 2, 0, 8, 208, 64376, 4294577440, 18446744043646083944
HalfLotus A003465 1, 1, 5, 109, 32297, 2147321017, 9223372023970362989
HalfLotusDrop 1, 0, 4, 104, 32188, 2147288720, 9223372021823041972
SmallLotus 1, 2, 10, 218, 64594, 4294642034, 18446744047940725978
SmallLotusDrop 1, 1, 8, 208, 64376, 4294577440, 18446744043646083944
NonDubSage A001320 0, 1, 3, 14, 240, 63488, 4227858432, 18302628885633695744
NonDubSageDrop 0, 1, 2, 11, 226, 63248, 4227794944, 18302628881405837312
NonLotus A005530 0, 2, 6, 38, 942, 325262, 25768825638, 129127208425774833206
NonLotusDrop 0, 2, 4, 32, 904, 324320, 25768500376, 129127208400006007568
HalfNonLotus A051381 0, 1, 3, 19, 471, 162631, 12884412819, 64563604212887416603
HalfNonLotusDrop 0, 1, 2, 16, 452, 162160, 12884250188, 64563604200003003784
SmallNonLotus 0, 1, 5, 37, 941, 325261, 25768825637, 129127208425774833205
SmallNonLotusDrop 0, 1, 4, 32, 904, 324320, 25768500376, 129127208400006007568
NonExAloe 0, 2, 8, 72, 3072, 1966208, 270499994624, 2342736474457787596800
NonExAloeDrop 0, 2, 6, 64, 3000, 1963136, 270498028416, 2342736474187287602176
HalfNonExAloe 0, 1, 4, 36, 1536, 983104, 135249997312, 1171368237228893798400
HalfNonExAloeDrop 0, 1, 3, 32, 1500, 981568, 135249014208, 1171368237093643801088
SmallNonExAloe A218384 0, 1, 7, 71, 3071, 1966207, 270499994623, 2342736474457787596799
SmallNonExAloeDrop 0, 1, 6, 64, 3000, 1963136, 270498028416, 2342736474187287602176
Primula A246537 1, 1, 3, 97, 32199, 2147318437, 9223372023969379707
PrimulaDrop 1, 0, 2, 94, 32102, 2147286238, 9223372021822061270
Eulerian numbers A000295 0, 0, 1, 4, 11, 26, 57, 120, 247, 502, 1013, 2036
DubSage 2, 2, 4, 32, 4096, 134217728, 288230376151711744
DubSageDrop 2, 0, 2, 28, 4064, 134213632, 288230376017494016
Sage ~A016031 1, 1, 2, 16, 2048, 67108864, 144115188075855872
SageDrop 1, 0, 1, 14, 2032, 67106816, 144115188008747008
TornSage ~A076688 1, 1, 8, 1024, 33554432, 72057594037927936
TornSageDrop 1, 0, 7, 1016, 33553408, 72057594004373504
Thyme A000231 2, 3, 7, 46, 4336, 134281216, 288230380379570176
ThymeDrop 2, 1, 4, 39, 4290, 134276880, 288230380245288960
Violet 1, 0, 2, 90, 31826, 2147158386, 9223372011085950170
half Violet for positive keys A007537 0, 1, 45, 15913, 1073579193, 4611686005542975085
Pansy A342286 2, 0, 2, 8, 210, 64384, 4294577650, 18446744043646148328
Peony A342287 0, 2, 0, 10, 208, 64386, 4294577648, 18446744043646148330
HalfPansy 1, 0, 1, 4, 105, 32192, 2147288825, 9223372021823074164
HalfPeony 0, 1, 0, 5, 104, 32193, 2147288824, 9223372021823074165
Chrysanthemum A006125 1, 1, 2, 8, 64, 1024, 32768, 2097152
Ranunculus A028361 1, 2, 6, 30, 270, 4590, 151470, 9845550
RanunculusDrop A126391 1, 1, 4, 24, 240, 4320, 146880, 9694080
TornRanunculus A028362 1, 1, 3, 15, 135, 2295, 75735, 4922775
TornRanunculusDrop A028362 1, 0, 2, 12, 120, 2160, 73440, 4847040
torn TornRanunculusDrop A353196 1, 6, 60, 1080, 36720, 2423520
row sums of Bramble 2, 6, 32, 440, 71104, 4297108096
half row sums of Bramble 1, 3, 16, 220, 35552, 2148554048
row sums of SmallBramble 1, 4, 26, 410, 70834, 4297112728, 18446744344381514834
torn row sums of SmallBramble 2, 13, 205, 35417, 2148556364, 9223372172190757417
Mimosa A003462 0, 1, 4, 13, 40, 121, 364, 1093, 3280
BigMimosa A007051 1, 2, 5, 14, 41, 122, 365, 1094, 3281
LongFern 0, 1, 3, 9, 27, 81, 243, 729, 2187
Fern A000244 1, 3, 9, 27, 81, 243, 729, 2187, 6561
FernDrop A025192 1, 2, 6, 18, 54, 162, 486, 1458, 4374
Saffron 0, 1, 3, 14, 870, 18796230
SaffronDrop 0, 1, 2, 11, 856, 18795360
Agave 0, 1, 0, 7, 750, 18771864
ExAgave 0, 2, 0, 56, 12000, 600699648
NonAgave 2, 0, 2, 16, 3154, 115384420
Dedekind A000372 2, 3, 6, 20, 168, 7581, 7828354
DedekindDrop 2, 1, 3, 14, 148, 7413, 7820773
Goldenrod A003182 2, 3, 5, 10, 30, 210, 16353
GoldenrodDrop A006602 2, 1, 2, 5, 20, 180, 16143
DubAnise A003180 2, 4, 12, 80, 3984, 37333248
DubAniseDrop A003181 2, 2, 8, 68, 3904, 37329264
Anise A000612 1, 2, 6, 40, 1992, 18666624
AniseDrop A055621 1, 1, 4, 34, 1952, 18664632
TornAnise ~A002857 1, 1, 3, 20, 996, 9333312
TornAniseDrop 1, 0, 2, 17, 976, 9332316
row sums of EmeraldSlab 1, 2, 5, 23, 1027, 19127963
Lily 2, 1, 3, 32, 4184, 134259939
Sesame ~A037293 0, 2, 6, 70, 12870, 601080390
SesameDrop 0, 2, 4, 64, 12800, 601067520
Chamomile 0, 1, 1, 8, 828, 18791995
Calendula A378302 0, 2, 2, 58, 12618, 601016690
row sums of Oleander 0, 2, 10, 94, 13194, 601145510
row sums of OleanderDrop 0, 2, 8, 84, 13100, 601132316
row sums of Olearia 0, 1, 5, 26, 948, 18800755
row sums of OleariaDrop 0, 1, 4, 21, 922, 18799807
triangles
name OEIS row 5 row sums
Cedar 2, 20, 160, 2560, 327680, 4294967296 Crocus
CedarDrop 0, 4, 64, 1536, 262144, 4294967296 CrocusDrop
HalfCedar 1, 10, 80, 1280, 163840, 2147483648 HalfCrocus
HalfCedarDrop 0, 2, 32, 768, 131072, 2147483648 HalfCrocusDrop
SignedCedar Lotus
HalfSignedCedar HalfLotus
Bramble 2048, 7936, 19840, 79360, 2031616, 4294967296
SignedBramble ExAloe
SmallBramble 1024, 5952, 18600, 79050, 2031585, 4294967295
SignedSmallBramble SmallExAloe
Forsythia 1, 62, 3565, 605120, 4158844804, 288230371925149328 Dandelion
ForsythiaDrop 0, 32, 2760, 546560, 4024688520, 288230371925149328 DandelionDrop
Hickory 0, 10, 60, 380, 4710, 325262 Hyacinth
HickoryDrop 0, 2, 24, 228, 3768, 325262 HyacinthDrop
Olive A227725 2, 31, 310, 3565, 121024, 134156284 Thyme
OliveDrop 0, 16, 240, 3220, 117120, 134156284 ThymeDrop
ExOlive 2, 62, 1240, 28520, 1936384, 4293001088 Grass
ExOliveDrop 0, 32, 960, 25760, 1873920, 4293001088 GrassDrop
TurnedExOlive 4293001088, 1936384, 28520, 1240, 62, 2 Grass
TurnedExOliveDrop 4292938624, 1933624, 28240, 1210, 60, 2 GrassDrop
SmallTurnedExOlive 4293001088, 1936384, 28520, 1240, 62, 1 SmallGrass
SmallTurnedExOliveDrop 4292938624, 1933624, 28240, 1210, 60, 1 SmallGrassDrop
Rhododendron 1, 31, 310, 1240, 1984, 1024 Ranunculus
RhododendronDrop 0, 16, 240, 1120, 1920, 1024 RanunculusDrop
TurnedRhododendron 1024, 1984, 1240, 310, 31, 1 Ranunculus
TurnedRhododendronDrop 960, 1864, 1170, 295, 30, 1 RanunculusDrop
SignedRhododendron
Robinia 1, 0, 20, 900, 159130, 2147158386 Primula
RobiniaDrop 0, 0, 8, 540, 127304, 2147158386 PrimulaDrop
Willow 2, 10, 100, 2180, 322970, 4294642034 Grass
WillowDrop 0, 2, 40, 1308, 258376, 4294642034 GrassDrop
HalfWillow 1, 5, 50, 1090, 161485, 2147321017 HalfGrass
HalfWillowDrop 0, 1, 20, 654, 129188, 2147321017 HalfGrassDrop
TurnedWillow 4294642034, 322970, 2180, 100, 10, 2 Grass
TurnedWillowDrop 4294577440, 322098, 2120, 92, 8, 2 GrassDrop
SmallTurnedWillow 4294642034, 322970, 2180, 100, 10, 1 SmallGrass
SmallTurnedWillowDrop 4294577440, 322098, 2120, 92, 8, 1 SmallGrassDrop
Chestnut 2, 0, 20, 80, 1050, 64384 ~Grass
ChestnutDrop 0, 0, 8, 48, 840, 64384 ~GrassDrop
Chinkapin 0, 10, 0, 100, 1040, 64386 ~Grass
ChinkapinDrop 0, 2, 0, 60, 832, 64386 ~GrassDrop
half Chestnut 1, 0, 10, 40, 525, 32192 ~HalfGrass
half ChestnutDrop 0, 0, 4, 24, 420, 32192 ~HalfGrassDrop
half Chinkapin 0, 5, 0, 50, 520, 32193 ~HalfGrass
half ChinkapinDrop 0, 1, 0, 30, 416, 32193 ~HalfGrassDrop
ExPascal A013609 1, 10, 40, 80, 80, 32 Fern
ExPascalDrop ~A370469 0, 2, 16, 48, 64, 32 FernDrop
TurnedExPascal A038207 32, 80, 80, 40, 10, 1 Fern
TurnedExPascalDrop A200139 16, 48, 56, 32, 9 1 FernDrop
Laurel A227724 0, 31, 0, 1085, 23250, 18771864 Saffron
LaurelDrop 0, 16, 0, 980, 22500, 18771864 SaffronDrop
ExLaurel 0, 62, 0, 8680, 372000, 600699648 Sesame
ExLaurelDrop 0, 32, 0, 7840, 360000, 600699648 SesameDrop
A211344 65535, 16711935, 252645135, 858993459, 1431655765
EmeraldSlab 1, 18796230, 330460, 1240, 31, 1
Lemon 0, 1, 80, 2070, 101504, 134156284 Lily
ExLemon 0, 2, 320, 16560, 1624064, 4293001088 Lotus
Orange 0, 1, 0, 630, 19500, 18771864 Chamomile
ExOrange 0, 2, 0, 5040, 312000, 600699648 Calendula
Oleander 0, 10, 60, 700, 64350, 601080390
OleanderDrop 0, 2, 24, 420, 51480, 601080390
SignedOleander Calendula
Olearia 0, 5, 30, 140, 4350, 18796230
OleariaDrop 0, 1, 12, 84, 3480, 18796230
SignedOlearia Chamomile


Seals

pairs
house sizes houses rooms seals blocks
smallest GCD
sequences a Valerian
ValerianDrop
Nepeta
NepetaDrop
Clover
Heather
Calluna
MaimedClover
Daisy
Dahlia
ShortDahlia
ShortDahliaDrop
triangles a, d Juniper
JuniperDrop
Thuja
ThujaDrop
Elm
Lime
Yew
MaimedElm
Oak
OakDrop
ExOak
ExOakDrop
a, v Sloe
SloeDrop
StackedHeather
DiagonalHeather
Rowan
MaimedStackedHeather
Ash
Aspen
a, g TurnedSloe
TurnedSloeDrop
SlopedHeather
SlopedLavender
Elder
MaimedSlopedHeather
TwistedAsh
Alder
pyramids a, d, v StackedLime
DiagonalLime
Liana
Ivy
a, d, g SlopedLime
SlopedMagnolia
TwistedLiana
Lonicera
hyper-
pyramids
a, d, v, g Syringa
SyringaDrop
Buddleja
BuddlejaDrop
Wisteria
WisteriaDrop
Petrea
MaimedWisteria
Jacaranda
JacarandaDrop
  • Triangle Magnolia appears in hyperpyramid Wisteria, but does not seem to count anything on its own. Its row sums are Lavender.
  • Triangle Birch is the number of seals by a=v and d. Its row sums are Aster.
  • Triangles TwistedBirch/TwistedBirchDrop are the number of seals with g=0 by a and d. Their row sums are Aster/AsterDrop.


a 🌊 arity
💧 adicity
d depth
v valency
g gravity

Arity n is short for adicityn.
Sequences, triangles and pyramids using arity are marked with a wave 🌊, those using adicity are marked with a drop 💧.
🌊 entries are sums of 💧 columns.


sequences
name OEIS entries
Rose A190939 1, 3, 5, 9, 15, 17, 33, 51, 65, 85, 105, 129, 153, 165, 195, 255
Tulip 1, 3, 5, 7, 15, 17, 19, 21, 23, 51, 63, 85, 95, 119, 127, 255
Aster A135922 1, 1, 2, 6, 26, 158, 1330, 15414
AsterDrop 1, 0, 1, 4, 20, 132, 1172, 14084
Daisy A006116 1, 2, 5, 16, 67, 374, 2825, 29212
Dahlia ~A182176 1, 1, 3, 11, 51, 307, 2451, 26387
Clover A076766 1, 2, 4, 8, 16, 32, 68, 148
Heather ~A034343 1, 1, 2, 4, 8, 16, 36, 80
Lavender 1, 0, 1, 2, 4, 8, 20, 44
ShortDahlia A182176 1, 3, 11, 51, 307, 2451, 26387, 387987
ShortDahliaDrop 1, 2, 8, 40, 256, 2144, 23936, 361600
Valerian 1, 2, 5, 16, 61, 264, 1225, 5790
ValerianDrop 1, 1, 3, 11, 45, 203, 961, 4565
Calluna 1, 2, 5, 12, 27, 58, 125, 272
MaimedClover 1, 1, 3, 7, 15, 31, 67, 147
Nepeta 1, 2, 5, 16, 61, 254, 1085, 4592
NepetaDrop 1, 1, 3, 11, 45, 193, 831, 3507
Salvia 1, 2, 4, 8, 17, 42, 204, 2064
Gardenia 1, 0, 1, 2, 5, 22, 37, 104
Gladiolus 1, 0, 1, 2, 5, 12, 17, 26
Ginger 1, 0, 1, 2, 5, 16, 137, 1698
Geranium A323842 1, 0, 1, 2, 11, 72, 677, 8686
Ambrosia 1, 1, 2, 6, 20, 78, 300, 1092
AmbrosiaDrop 1, 0, 1, 4, 14, 58, 222, 792
Akanthus 1, 1, 2, 6, 20, 68, 220, 664
AkanthusDrop 1, 0, 1, 4, 14, 48, 152, 444
Aconite 1, 1, 2, 4, 9, 25, 162, 1860
triangles
name OEIS row 5 row sums
Birch ~A139382 0, 1, 40, 90, 26, 1 Aster
symmetric Oak A022166 1, 31, 155, 155, 31, 1 Daisy
OakDrop ~A289537 0, 16, 120, 140, 30, 1 Dahlia
Ash 1, 5, 20, 60, 130, 158 Daisy
Aspen 0, 1, 8, 36, 104, 158 Dahlia
TwistedAsh 158, 130, 60, 20, 5, 1 Daisy
Alder 132, 106, 48, 16, 4, 1 Dahlia
symmetric Elm A076831 1, 5, 10, 10, 5, 1 Clover
Lime ~A034253 0, 1, 4, 6, 4, 1 Heather
~A076832 0, 1, 5, 11, 15, 16
ExOak ~A289537 1, 62, 620, 1240, 496, 32 ShortDahlia
~symmetric ExOakDrop 0, 32, 480, 1120, 480, 32 ShortDahliaDrop
TwistedBirch ~A139382 1, 26, 90, 40, 1, 0 Aster
TwistedBirchDrop 0, 15, 77, 39, 1, 0 AsterDrop
Yew 1, 15, 20, 15, 6, 1 Calluna
MaimedElm 0, 5, 10, 10, 5, 1 MaimedClover
Elder 27, 16, 8, 4, 2, 1 Calluna
MaimedSlopedHeather 15, 8, 4, 2, 1, 1 MaimedClover
symmetric Juniper 1, 31, 100, 100, 31, 1 Valerian
JuniperDrop 0, 16, 71, 85, 30, 1 ValerianDrop
TurnedLime ~A034253 1, 4, 6, 4, 1, 0 Heather
symmetric Magnolia 0, 1, 3, 3, 1, 0 Lavender
Rowan 1, 5, 8, 12, 16, 16 Calluna
MaimedStackedHeather 0, 1, 2, 4, 8, 16 MaimedClover
Sloe 1, 5, 20, 60, 100, 78 Valerian
SloeDrop 0, 1, 8, 36, 80, 78 ValerianDrop
TurnedSloe 78, 100, 60, 20, 5, 1 Valerian
TurnedSloeDrop 58, 76, 48, 16, 4, 1 ValerianDrop
StackedHeather 1, 1, 2, 4, 8, 16 Clover
DiagonalHeather 0, 0, 0, 0, 0, 16 Heather
SlopedHeather 16, 8, 4, 2, 1, 1 Clover
SlopedLavender 8, 4, 2, 1, 0, 1 Heather
Fir 1, 0, 10, 20, 25, 22 Ambrosia
FirDrop 0, 0, 4, 12, 20, 22 AmbrosiaDrop
TurnedFir 22, 25, 20, 10, 0, 1 Ambrosia
Spruce 1, 0, 10, 20, 25, 12 Akanthus
SpruceDrop 0, 0, 4, 12, 20, 12 AkanthusDrop
TurnedSpruce 12, 25, 20, 10, 0, 1 Akanthus
SlopedGinger 16, 5, 2, 1, 0, 1 Aconite
Pine 1, 0, 10, 20, 55, 72 Aster
PineDrop 0, 0, 4, 12, 44, 72 AsterDrop
TurnedPine 72, 55, 20, 10, 0, 1 Aster
Hawthorn 0, 1, 15, 35, 26, 1 Ambrosia
Buckthorn 0, 1, 10, 30, 26, 1 Akanthus
Holly 0, 1, 8, 11, 4, 1 Aconite
symmetric Thuja 1, 31, 95, 95, 31, 1 Nepeta
ThujaDrop 0, 16, 66, 80, 30, 1 NepetaDrop
symmetric Buxus 1, 5, 15, 15, 5, 1 Salvia