A303896 - OEIS

%I #4 May 02 2018 08:06:02

%S 0,1,1,1,7,1,2,23,23,2,3,86,54,86,3,5,313,271,271,313,5,8,1145,842,

%T 1659,842,1145,8,13,4184,3420,7421,7421,3420,4184,13,21,15293,11916,

%U 39711,29479,39711,11916,15293,21,34,55895,45404,195279,200144,200144,195279

%N 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.

%C Table starts

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

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

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

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

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

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

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

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

%C .21.55895.163979.5056641.32529473.462257363.4824517709.56970820993.668263785713

%H R. H. Hardin, <a href="/A303896/b303896.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

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

%F k=3: [order 13] for n>14

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

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

%e Some solutions for n=5 k=4

%e ..0..0..0..1. .0..1..0..1. .0..0..1..1. .0..0..1..0. .0..1..1..0

%e ..0..1..1..1. .1..1..1..0. .1..0..0..0. .0..1..1..1. .0..1..1..1

%e ..1..1..1..1. .1..1..0..0. .0..1..0..0. .1..1..1..1. .1..0..1..1

%e ..1..0..0..0. .1..0..0..0. .1..1..1..1. .1..1..1..0. .0..0..0..1

%e ..0..0..0..1. .1..0..0..1. .0..1..0..0. .0..0..1..0. .1..0..1..0

%Y Column 1 is A000045(n-1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 02 2018