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URL: https://oeis.org/A303896

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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.
8
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 02 2018
STATUS
approved