cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A302427 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 11, 10, 16, 13, 25, 21, 21, 21, 32, 21, 65, 38, 42, 51, 42, 64, 34, 185, 88, 83, 148, 93, 86, 128, 55, 385, 188, 235, 372, 362, 207, 179, 256, 89, 649, 377, 532, 1359, 992, 879, 517, 370, 512, 144, 1489, 735, 1250, 4223, 4231, 2503, 2447
Offset: 1

Views

Author

R. H. Hardin, Apr 07 2018

Keywords

Comments

Table starts
...1...2....3....5.....8.....13.....21......34.......55........89........144
...2...3....9...17....25.....65....185.....385......649......1489.......3929
...4...6...11...21....38.....88....188.....377......735......1557.......3288
...8..10...21...42....83....235....532....1250.....2839......6972......16274
..16..21...51..148...372...1359...4223...12765....36991....120577.....379049
..32..42...93..362...992...4231..14764...53851...182216....685166....2496115
..64..86..207..879..2503..12527..48037..204549...775916...3358602...13687791
.128.179..517.2447..7611..49454.227283.1171867..5110314..27366139..134037982
.256.370.1007.6306.21321.179252.940829.6104653.30957683.207165078.1213329113

Examples

			Some solutions for n=5 k=4
..0..0..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .1..1..0..1. .0..1..0..0. .1..1..0..1
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..0..0..1. .1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..0
..1..0..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302164.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: a(n) = a(n-1) +10*a(n-3) -8*a(n-4) for n>9
k=4: [order 42] for n>43
k=5: [order 21] for n>24
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
n=3: [order 18] for n>19
n=4: [order 68] for n>69

A302635 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 8, 10, 16, 13, 25, 14, 19, 21, 32, 21, 65, 25, 33, 42, 42, 64, 34, 185, 47, 65, 101, 82, 86, 128, 55, 385, 83, 149, 257, 248, 189, 179, 256, 89, 649, 150, 304, 691, 719, 657, 469, 370, 512, 144, 1489, 269, 643, 1734, 2262, 2303, 1841, 1029
Offset: 1

Views

Author

R. H. Hardin, Apr 10 2018

Keywords

Comments

Table starts
...1...2....3....5.....8.....13.....21......34.......55.......89.......144
...2...3....9...17....25.....65....185.....385......649.....1489......3929
...4...6....8...14....25.....47.....83.....150......269......488.......876
...8..10...19...33....65....149....304.....643.....1343.....2880......6038
..16..21...42..101...257....691...1734....4502....11524....30121.....77399
..32..42...82..248...719...2262...6460...19799....59002...179668....535412
..64..86..189..657..2303...8981..30216..112431...408512..1512824...5441957
.128.179..469.1841..7695..35772.144266..652931..2863575.12800635..55765517
.256.370.1029.4892.24205.135125.642553.3499587.18446157.98898783.515558643

Examples

			Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..0..1..1. .0..1..0..1
..1..1..1..0. .0..1..0..1. .0..1..0..0. .0..1..0..1. .0..0..0..1
..0..0..0..0. .0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..1..1. .0..1..0..1. .0..0..1..0. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .1..1..1..0. .0..0..1..1. .0..1..1..0

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302164.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: a(n) = a(n-1) +9*a(n-3) -4*a(n-4) +2*a(n-5) -10*a(n-6) +4*a(n-7) +4*a(n-9) for n>13
k=4: [order 21] for n>25
k=5: [order 29] for n>32
k=6: [order 54] for n>65
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
n=3: a(n) = a(n-1) +a(n-2) +2*a(n-4) -a(n-5) for n>7
n=4: [order 22] for n>23
n=5: [order 63] for n>64
n=6: [order 81] for n>86

A303197 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 9, 6, 8, 8, 17, 12, 10, 16, 13, 25, 23, 23, 21, 32, 21, 65, 43, 46, 62, 42, 64, 34, 185, 105, 97, 185, 122, 86, 128, 55, 385, 233, 283, 523, 497, 305, 179, 256, 89, 649, 479, 687, 2106, 1751, 1357, 793, 370, 512, 144, 1489, 968, 1642, 7425, 8250, 5573
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2018

Keywords

Comments

Table starts
...1...2....3.....5.....8.....13......21.......34........55.........89
...2...3....9....17....25.....65.....185......385.......649.......1489
...4...6...12....23....43....105.....233......479.......968.......2146
...8..10...23....46....97....283.....687.....1642......3949......10169
..16..21...62...185...523...2106....7425....23976.....77199.....278516
..32..42..122...497..1751...8250...34801...138014....547379....2363422
..64..86..305..1357..5573..32223..164295...791150...3806973...20061588
.128.179..793..4207.21575.159440.1053249..6303961..38494616..258640170
.256.370.1757.12167.76833.703465.5803057.43287208.332058205.2785202370

Examples

			Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..0
..1..1..1..0. .0..1..1..1. .0..0..0..1. .0..1..0..0. .0..1..0..1
..1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..1..0..1..0. .0..0..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..1
..1..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..1..1

Links

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).
Row 2 is A302164.

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 7] for n>11
k=4: [order 42] for n>43
k=5: [order 33] for n>37
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +16*a(n-4) -8*a(n-5) for n>6
n=3: [order 18] for n>19
n=4: [order 70] for n>71
Showing 1-3 of 3 results.

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