A305288 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4 or 8 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 55, 86, 3, 5, 313, 279, 279, 313, 5, 8, 1145, 895, 1763, 895, 1145, 8, 13, 4184, 3696, 8431, 8431, 3696, 4184, 13, 21, 15293, 13289, 46983, 41446, 46983, 13289, 15293, 21, 34, 55895, 51734, 246893, 301533, 301533, 246893

Offset

1,5

Comments

Table starts

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

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

..1....23.....55.....279......895.......3696.......13289........51734

..2....86....279....1763.....8431......46983......246893......1332201

..3...313....895....8431....41446.....301533.....1847322.....12314089

..5..1145...3696...46983...301533....2636906....21092843....175328455

..8..4184..13289..246893..1847322...21092843...214220078...2256259549

.13.15293..51734.1332201.12314089..175328455..2256259549..29751215558

.21.55895.192418.7128691.80678010.1483162272.24509450800.412395328914

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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 36] for n>41

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A303890.

Sequence in context: A316130 A317436 A303896 * A304901 A316583 A304597

Adjacent sequences: A305285 A305286 A305287 * A305289 A305290 A305291

Keyword

nonn,tabl

Author

R. H. Hardin, May 29 2018

Status

approved