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.

A302472 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 49, 34, 0, 5, 146, 203, 250, 111, 0, 8, 537, 955, 1401, 1147, 361, 0, 13, 1934, 4556, 10264, 8493, 5486, 1172, 0, 21, 6861, 21843, 78679, 101109, 53575, 25599, 3809, 0, 34, 24386, 103319, 584333, 1141147, 990266, 331044
Offset: 1

Views

Author

R. H. Hardin, Apr 08 2018

Keywords

Comments

Table starts
.0.....1......1........2.........3...........5.............8..............13
.0.....3.....14.......45.......146.........537..........1934............6861
.0....11.....49......203.......955........4556.........21843..........103319
.0....34....250.....1401.....10264.......78679........584333.........4330427
.0...111...1147.....8493....101109.....1141147......12546601.......139759054
.0...361...5486....53575....990266....16983273.....278275383......4682106140
.0..1172..25599...331044...9731423...251512646....6145486847....156721340433
.0..3809.121626..2075845..96648626..3770915891..137317050228...5300304476103
.0.12377.572657.12918219.950374395.55956081186.3037409718914.177368160967073

Examples

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

Links

Crossrefs

Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A302225.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 43] for n>44
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
n=3: [order 19] for n>21
n=4: [order 63] for n>66

A302670 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 43, 34, 0, 5, 146, 164, 194, 111, 0, 8, 537, 760, 934, 691, 361, 0, 13, 1934, 3425, 6110, 4267, 2802, 1172, 0, 21, 6861, 15569, 38736, 42367, 21949, 10660, 3809, 0, 34, 24386, 70323, 251254, 352174, 316977, 106793, 41839
Offset: 1

Views

Author

R. H. Hardin, Apr 11 2018

Keywords

Comments

Table starts
.0.....1......1.......2.........3..........5............8............13
.0.....3.....14......45.......146........537.........1934..........6861
.0....11.....43.....164.......760.......3425........15569.........70323
.0....34....194.....934......6110......38736.......251254.......1610569
.0...111....691....4267.....42367.....352174......3204956......28324200
.0...361...2802...21949....316977....3640304.....46360666.....582115385
.0..1172..10660..106793...2320879...35549458....637088915...11181864782
.0..3809..41839..529984..17037458..353912413...8880747825..219692176894
.0.12377.161878.2617548.125456575.3503182605.123521424862.4291098950499

Examples

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

Links

Crossrefs

Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A302225.
Row 3 is A302226.
Row 4 is A302227.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 32] for n>35
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
n=3: [order 15] for n>17
n=4: [order 54] for n>58

A303254 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 1, 0, 1, 3, 0, 2, 14, 11, 0, 3, 45, 49, 34, 0, 5, 146, 203, 250, 111, 0, 8, 537, 955, 1401, 1183, 361, 0, 13, 1934, 4556, 10264, 8664, 5918, 1172, 0, 21, 6861, 21843, 78679, 106803, 55624, 28680, 3809, 0, 34, 24386, 103319, 584333, 1218385, 1105676, 349273
Offset: 1

Views

Author

R. H. Hardin, Apr 20 2018

Keywords

Comments

Table starts
.0.....1......1........2..........3...........5.............8..............13
.0.....3.....14.......45........146.........537..........1934............6861
.0....11.....49......203........955........4556.........21843..........103319
.0....34....250.....1401......10264.......78679........584333.........4330427
.0...111...1183.....8664.....106803.....1218385......13529019.......153269484
.0...361...5918....55624....1105676....19457754.....322544617......5622650429
.0..1172..28680...349273...11394429...306224454....7600681910....204093228252
.0..3809.141255..2229806..118856245..4895684572..181926316054...7516309079483
.0.12377.691968.14141138.1230109648.77683246701.4319287740641.274539947294004

Examples

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

Links

Crossrefs

Column 2 is A180762.
Row 1 is A000045(n-1).
Row 2 is A302225.
Row 3 is A302473.
Row 4 is A302474.

Formula

Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4)
k=3: [order 14]
k=4: [order 43] for n>44
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6
n=3: [order 19] for n>21
n=4: [order 63] for n>66
Showing 1-3 of 3 results.

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