A304901 T(n,k) = Number of n X k 0..1 arrays with every element unequal to 1, 2, 3, 4 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 62, 86, 3, 5, 313, 330, 330, 313, 5, 8, 1145, 1249, 2373, 1249, 1145, 8, 13, 4184, 5562, 13954, 13954, 5562, 4184, 13, 21, 15293, 23101, 88308, 107723, 88308, 23101, 15293, 21, 34, 55895, 99064, 546357, 946723, 946723, 546357

Offset

1,5

Comments

Table starts

..0.....1......1........2.........3...........5............8.............13

..1.....7.....23.......86.......313........1145.........4184..........15293

..1....23.....62......330......1249........5562........23101..........99064

..2....86....330.....2373.....13954.......88308.......546357........3395402

..3...313...1249....13954....107723......946723......8143342.......69406724

..5..1145...5562....88308....946723....11067544....132134627.....1529832969

..8..4184..23101...546357...8143342...132134627...2256313057....36576467823

.13.15293..99064..3395402..69406724..1529832969..36576467823...816589152784

.21.55895.418753.21113828.599014812.18095801753.611064999079.18937183868022

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2);

k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4);

k=3: [order 15] for n>16;

k=4: [order 46] for n>48.

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A303890.

Sequence in context: A317436 A303896 A305288 * A316583 A304597 A316383

Adjacent sequences: A304898 A304899 A304900 * A304902 A304903 A304904

Keyword

nonn,tabl

Author

R. H. Hardin, May 20 2018

Status

approved