A303896 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 4 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 7, 1, 2, 23, 23, 2, 3, 86, 54, 86, 3, 5, 313, 271, 271, 313, 5, 8, 1145, 842, 1659, 842, 1145, 8, 13, 4184, 3420, 7421, 7421, 3420, 4184, 13, 21, 15293, 11916, 39711, 29479, 39711, 11916, 15293, 21, 34, 55895, 45404, 195279, 200144, 200144, 195279

Offset

1,5

Comments

Table starts

..0.....1......1.......2........3.........5..........8..........13...........21

..1.....7.....23......86......313......1145.......4184.......15293........55895

..1....23.....54.....271......842......3420......11916.......45404.......163979

..2....86....271....1659.....7421.....39711.....195279.....1003855......5056641

..3...313....842....7421....29479....200144.....992789.....5930552.....32529473

..5..1145...3420...39711...200144...1541443....9758243....68015993....462257363

..8..4184..11916..195279...992789...9758243...71307109...596704142...4824517709

.13.15293..45404.1003855..5930552..68015993..596704142..5846922441..56970820993

.21.55895.163979.5056641.32529473.462257363.4824517709.56970820993.668263785713

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

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 13] for n>14

k=4: [order 35] for n>40

k=5: [order 92] for n>98

Example

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

Crossrefs

Column 1 is A000045(n-1).

Sequence in context: A316448 A316130 A317436 * A305288 A304901 A316583

Adjacent sequences: A303893 A303894 A303895 * A303897 A303898 A303899

Keyword

nonn,tabl

Author

R. H. Hardin, May 02 2018

Status

approved