Wikiversity

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

name OEIS description 🌊 ↔ πŸ’§ children entries
2 🌊 Fir (a, lw) ↦ BF Larch row sums Grass
2 πŸ’§ Larch (a, lw) ↦ BF Fir row sums Moss
2 🌊 Pine (a, cw) ↦ BF Spruce row sums Grass
2 πŸ’§ Spruce (a, cw) ↦ BF Pine row sums Moss
1 🌊 Grass A001146 a ↦ BF Moss 2, 4, 16, 256, 65536
1 πŸ’§ Moss ~A111403 a ↦ BF Grass 2, 2, 12, 240, 65280
1 🌊 SmallGrass ~A058891 SmallMoss 1, 2, 8, 128, 32768
1 πŸ’§ SmallMoss ~A040996 SmallGrass 1, 1, 6, 120, 32640
1 🌊 Maitake A318130 column 0 of Fir 2, 1, 8, 208, 64376 2, 3, 11, 219, 64595
1 🌊 Meshima column 0 of Pine
SmallMeshima + 1 		2, 1, 6, 176, 62280 2, 3, 9, 185, 62465
1 🌊 Crocus Hibiscus 2, 6, 26, 318, 66674
1 πŸ’§ Hibiscus Crocus 2, 4, 20, 292, 66356
1 🌊 SmallCrocus A246418 a ↦ β™‚ BF SmallHibiscus 1, 3, 13, 159, 33337
1 πŸ’§ SmallHibiscus a ↦ β™‚ BF SmallCrocus 1, 2, 10, 146, 33178
1 🌊 Primula A246537 a ↦ ♀ BF Petunia 1, 1, 3, 97, 32199
1 πŸ’§ Petunia a ↦ ♀ BF Primula 1, 0, 2, 94, 32102
1 β™‚ Π– 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 35, 48
1 ♀ Π– 0, 6, 7, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 37
2 🌊 Willow (a, v) ↦ BF Poplar row sums Grass
diagonal Lotus
2 πŸ’§ Poplar (a, v) ↦ BF Willow row sums Moss
diagonal Lotus
2 🌊 SmallWillow SmallPoplar RS SmallGrass, D SmallLotus
2 πŸ’§ SmallPoplar SmallWillow RS SmallMoss, D SmallLotus
2 🌊 Cedar Cypress RS Crocus, D Grass
2 πŸ’§ Cypress Cedar RS Hibiscus, D Grass
2 🌊 SmallCedar (a, v) ↦ β™‚ BF SmallCypress row sums SmallCrocus
diagonal SmallGrass
2 πŸ’§ SmallCypress (a, v) ↦ β™‚ BF SmallCedar row sums SmallHibiscus
diagonal SmallGrass
2 🌊 Robinia (a, v) ↦ ♀ BF Acacia row sums Primula
diagonal Violet
2 πŸ’§ Acacia (a, v) ↦ ♀ BF Robinia row sums Petunia
diagonal Violet
2 🌊 Chestnut (a, v) ↦ β™‚βˆ’β™€ BF
SmallCedar βˆ’ Robinia 		Chinkapin row sums Mallow
diagonal Orchid
2 πŸ’§ Chinkapin (a, v) ↦ β™‚βˆ’β™€ BF
SmallCypress βˆ’ Acacia 		Chestnut row sums Mullein
diagonal Orchid
1 🌊 Mallow a ↦ β™‚βˆ’β™€ BF
SmallCrocus βˆ’ Primula
Crocus βˆ’ Grass 		Mullein 0, 2, 10, 62, 1138, 330422
1 SmallMallow A059301 (filter bases of an n-set) 0, 1, 5, 31, 569, 165211
1 πŸ’§ Mullein a ↦ β™‚βˆ’β™€ BF
SmallHibiscus βˆ’ Petunia
Hibiscus βˆ’ Moss 		Mallow 0, 2, 8, 52, 1076, 329284
1 Orchid A005530 SmallGrass βˆ’ Violet
Grass βˆ’ Lotus 		0, 2, 6, 38, 942, 325262
1 SmallOrchid A051381 0, 1, 3, 19, 471, 162631
2 SignedCedar row sums Lotus
diagonal Grass
2 SmallSignedCedar RS SmallLotus, D SmallGrass
1 🌊 Lotus A000371 a ↦ dense BF
inverse binomial transform of Grass 		Lily 2, 2, 10, 218, 64594, 4294642034
1 🌊 SmallLotus A003465 SmallLily 1, 1, 5, 109, 32297, 2147321017
1 πŸ’§ Lily a ↦ dense BF Lotus 2, 0, 8, 208, 64376, 4294577440
1 πŸ’§ SmallLily SmallLotus 1, 0, 4, 104, 32188, 2147288720
1 Violet ~ 2Β·A007537 Lotus βˆ’ SmallGrass 1, 0, 2, 90, 31826, 2147158386
1 πŸ’§ A342286 a ↦ dense self-reverse BF
S(n) = Lotus(nβˆ’1) βˆ’ S(nβˆ’1) 		2, 2, 4, 12, 222, 64606 2, 0, 2, 8, 210, 64384
1 A327041 OR 0, 1, 2, 3, 3, 3, 3, 3, 4, 5, 6, 7, 7, 7, 7, 7
1 A261283 XOR long version A253315 0, 1, 2, 3, 3, 2, 1, 0, 4, 5, 6, 7, 7, 6, 5, 4


Seals

edit
name OEIS description 🌊 ↔ πŸ’§ children entries
1 Rose A190939 truth tables 1, 3, 5, 9, 15, 17, 33, 51, 65, 85, 105, 129, 153, 165, 195, 255
1 Tulip Zhegalkin indices 1, 3, 5, 7, 15, 17, 19, 21, 23, 51, 63, 85, 95, 119, 127, 255
3 πŸ’§ Ivy (a, d, v) ↦ # seals Liana layer sums Maple and Aspen
(with row sums Dahlia)
side Birch
2 πŸ’§ Maple ~A289537 (a, d) ↦ # seals Oak row sums Dahlia
2 πŸ’§ Aspen (a, v) ↦ # seals Ash row sums Dahlia
diagonal Aster
1 πŸ’§ Dahlia ~A182176 a ↦ # seals Daisy 1, 1, 3, 11, 51, 307, 2451, 26387
3 🌊 Liana (a, d, v) ↦ # seals Ivy layer sums Oak and Ash
(with row sums Daisy)
side Birch
2 🌊 Oak A022166 (a, d) ↦ # seals
symmetric triangle 		Maple row sums Daisy
2 🌊 Ash (a, v) ↦ # seals Aspen row sums Daisy
diagonal Aster
1 🌊 Daisy A006116 a ↦ # seals Dahlia 1, 2, 5, 16, 67, 374, 2825, 29212
2 πŸ’§ Lime A034253 (a, d) ↦ # EC Elm row sums Heather
1 πŸ’§ Heather ~A034343 a ↦ # EC Clover 1, 1, 2, 4, 8, 16, 36, 80
2 🌊 Elm A076831 (a, d) ↦ # EC
symmetric triangle 		Lime row sums Clover
1 🌊 Clover A076766 a ↦ # EC Heather 1, 2, 4, 8, 16, 32, 68, 148
2 Birch ~A139382 (a, d) ↦ # new seals row sums Aster
1 Aster A135922 a ↦ # new seals
inverse binomial transform of Daisy 		1, 1, 2, 6, 26, 158, 1330, 15414
2 🌊 MapleMinor ~A289537 (a, d) ↦ # blocks Sycamore row sums DahliaMinor
1 🌊 DahliaMinor A182176 a ↦ # blocks Azalea 1, 3, 11, 51, 307, 2451, 26387, 387987
2 πŸ’§ Sycamore (a, d) ↦ # blocks MapleMinor row sums Azalea
1 πŸ’§ Azalea a ↦ # blocks DahliaMinor 1, 2, 8, 40, 256, 2144, 23936, 361600
2 Beech ~A076832 ?
Difference of neighbors gives entry of Lime. 		row sums Poppy
diagonal Heather
1 Poppy ? 1, 1, 3, 8, 20, 48, 128, 326
2 πŸ’§ Alder (a, p) ↦ # seals reflected Ash row sums Dahlia
1 SmallMeshima A305737 ? Β Β  Meshima βˆ’ 1 1, 2, 8, 184, 62464

name pantry

edit
Retrieved from "https://en.wikiversity.org/w/index.php?title=Overview_of_sequences_related_to_Boolean_functions&oldid=2663548"