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
name | OEIS | description | π ↔ π§ | children | entries | ||
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2 | π | Fir | (a, lw) β¦ BF | Larch | row sums Grass | ||
2 | π§ | Larch | (a, lw) β¦ BF | Fir | row sums Moss | ||
2 | π | Pine | (a, cw) β¦ BF | Spruce | row sums Grass | ||
2 | π§ | Spruce | (a, cw) β¦ BF | Pine | row sums Moss | ||
1 | π | Grass | A001146 | a β¦ BF | Moss | 2, 4, 16, 256, 65536 | |
1 | π§ | Moss | ~A111403 | a β¦ BF | Grass | 2, 2, 12, 240, 65280 | |
1 | π | SmallGrass | ~A058891 | SmallMoss | 1, 2, 8, 128, 32768 | ||
1 | π§ | SmallMoss | ~A040996 | SmallGrass | 1, 1, 6, 120, 32640 | ||
1 | π | Maitake | A318130 | column 0 of Fir | 2, 1, 8, 208, 64376 | 2, 3, 11, 219, 64595 | |
1 | π | Meshima | column 0 of Pine SmallMeshima + 1 |
2, 1, 6, 176, 62280 | 2, 3, 9, 185, 62465 | ||
1 | π | Crocus | Hibiscus | 2, 6, 26, 318, 66674 | |||
1 | π§ | Hibiscus | Crocus | 2, 4, 20, 292, 66356 | |||
1 | π | SmallCrocus | A246418 | a β¦ β BF | SmallHibiscus | 1, 3, 13, 159, 33337 | |
1 | π§ | SmallHibiscus | a β¦ β BF | SmallCrocus | 1, 2, 10, 146, 33178 | ||
1 | π | Primula | A246537 | a β¦ β BF | Petunia | 1, 1, 3, 97, 32199 | |
1 | π§ | Petunia | a β¦ β 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 | β Π | 0, 6, 7, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 36, 37 | |||||
2 | π | Willow | (a, v) β¦ BF | Poplar | row sums Grass diagonal Lotus |
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2 | π§ | Poplar | (a, v) β¦ BF | Willow | row sums Moss diagonal Lotus |
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2 | π | SmallWillow | SmallPoplar | RS SmallGrass, D SmallLotus | |||
2 | π§ | SmallPoplar | SmallWillow | RS SmallMoss, D SmallLotus | |||
2 | π | Cedar | Cypress | RS Crocus, D Grass | |||
2 | π§ | Cypress | Cedar | RS Hibiscus, D Grass | |||
2 | π | SmallCedar | (a, v) β¦ β BF | SmallCypress | row sums SmallCrocus diagonal SmallGrass |
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2 | π§ | SmallCypress | (a, v) β¦ β BF | SmallCedar | row sums SmallHibiscus diagonal SmallGrass |
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2 | π | Robinia | (a, v) β¦ β BF | Acacia | row sums Primula diagonal Violet |
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2 | π§ | Acacia | (a, v) β¦ β BF | Robinia | row sums Petunia diagonal Violet |
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2 | π | Chestnut | (a, v) β¦ β−β BF SmallCedar − Robinia |
Chinkapin | row sums Mallow diagonal Orchid |
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2 | π§ | Chinkapin | (a, v) β¦ β−β BF SmallCypress − Acacia |
Chestnut | row sums Mullein diagonal Orchid |
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1 | π | Mallow | a β¦ β−β BF SmallCrocus − Primula Crocus − Grass |
Mullein | 0, 2, 10, 62, 1138, 330422 | ||
1 | SmallMallow | A059301 | (filter bases of an n-set) | 0, 1, 5, 31, 569, 165211 | |||
1 | π§ | Mullein | a β¦ β−β BF SmallHibiscus − Petunia Hibiscus − Moss |
Mallow | 0, 2, 8, 52, 1076, 329284 | ||
1 | Orchid | A005530 | SmallGrass − Violet Grass − Lotus |
0, 2, 6, 38, 942, 325262 | |||
1 | SmallOrchid | A051381 | 0, 1, 3, 19, 471, 162631 | ||||
2 | SignedCedar | row sums Lotus diagonal Grass |
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2 | SmallSignedCedar | RS SmallLotus, D SmallGrass | |||||
1 | π | Lotus | A000371 | a β¦ dense BF inverse binomial transform of Grass |
Lily | 2, 2, 10, 218, 64594, 4294642034 | |
1 | π | SmallLotus | A003465 | SmallLily | 1, 1, 5, 109, 32297, 2147321017 | ||
1 | π§ | Lily | a β¦ dense BF | Lotus | 2, 0, 8, 208, 64376, 4294577440 | ||
1 | π§ | SmallLily | SmallLotus | 1, 0, 4, 104, 32188, 2147288720 | |||
1 | Violet | ~ 2·A007537 | Lotus − SmallGrass | 1, 0, 2, 90, 31826, 2147158386 | |||
1 | π§ | A342286 | a β¦ dense self-reverse BF S(n) = Lotus(nβ1) β S(nβ1) |
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 | edit source]name | OEIS | description | π ↔ π§ | children | entries | ||
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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 | π§ | Ivy | (a, d, v) β¦ # seals | Liana | layer sums Maple and Aspen (with row sums Dahlia) side Birch |
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2 | π§ | Maple | ~A289537 | (a, d) β¦ # seals | Oak | row sums Dahlia | |
2 | π§ | Aspen | (a, v) β¦ # seals | Ash | row sums Dahlia diagonal Aster |
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1 | π§ | Dahlia | ~A182176 | a β¦ # seals | Daisy | 1, 1, 3, 11, 51, 307, 2451, 26387 | |
3 | π | Liana | (a, d, v) β¦ # seals | Ivy | layer sums Oak and Ash (with row sums Daisy) side Birch |
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2 | π | Oak | A022166 | (a, d) β¦ # seals symmetric triangle |
Maple | row sums Daisy | |
2 | π | Ash | (a, v) β¦ # seals | Aspen | row sums Daisy diagonal Aster |
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1 | π | Daisy | A006116 | a β¦ # seals | Dahlia | 1, 2, 5, 16, 67, 374, 2825, 29212 | |
2 | π§ | Lime | A034253 | (a, d) β¦ # EC | Elm | row sums Heather | |
1 | π§ | Heather | ~A034343 | a β¦ # EC | Clover | 1, 1, 2, 4, 8, 16, 36, 80 | |
2 | π | Elm | A076831 | (a, d) β¦ # EC symmetric triangle |
Lime | row sums Clover | |
1 | π | Clover | A076766 | a β¦ # EC | Heather | 1, 2, 4, 8, 16, 32, 68, 148 | |
2 | Birch | ~A139382 | (a, d) β¦ # new seals | row sums Aster | |||
1 | Aster | A135922 | a β¦ # new seals inverse binomial transform of Daisy |
1, 1, 2, 6, 26, 158, 1330, 15414 | |||
2 | π | MapleMinor | ~A289537 | (a, d) β¦ # blocks | Sycamore | row sums DahliaMinor | |
1 | π | DahliaMinor | A182176 | a β¦ # blocks | Azalea | 1, 3, 11, 51, 307, 2451, 26387, 387987 | |
2 | π§ | Sycamore | (a, d) β¦ # blocks | MapleMinor | row sums Azalea | ||
1 | π§ | Azalea | a β¦ # 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 |
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1 | Poppy | ? | 1, 1, 3, 8, 20, 48, 128, 326 | ||||
2 | π§ | Alder | (a, p) β¦ # seals | reflected Ash | row sums Dahlia | ||
1 | SmallMeshima | A305737 | ? Meshima − 1 | 1, 2, 8, 184, 62464 |
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