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%I #4 Mar 07 2018 07:34:54
%S 1,2,2,3,3,3,5,2,2,5,8,3,4,3,8,13,6,7,7,6,13,21,6,6,20,6,6,21,34,11,
%T 17,32,32,17,11,34,55,26,34,68,56,68,34,26,55,89,43,57,191,208,208,
%U 191,57,43,89,144,82,80,504,546,1162,546,504,80,82,144,233,178,164,1353,2006
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ..1..2..3....5....8....13.....21......34.......55........89........144
%C ..2..3..2....3....6.....6.....11......26.......43........82........178
%C ..3..2..4....7....6....17.....34......57.......80.......164........302
%C ..5..3..7...20...32....68....191.....504.....1353......4033......11685
%C ..8..6..6...32...56...208....546....2006.....5835.....18466......58308
%C .13..6.17...68..208..1162...4067...20265....88836....420674....1978897
%C .21.11.34..191..546..4067..17412..112660...634311...3789374...21768434
%C .34.26.57..504.2006.20265.112660.1045409..7841480..64468772..513205097
%C .55.43.80.1353.5835.88836.634311.7841480.76908966.836417456.8738195507
%H R. H. Hardin, <a href="/A300506/b300506.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) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) +a(n-5) -2*a(n-6) +a(n-7)
%F k=3: [order 26] for n>31
%F k=4: [order 93] for n>103
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..1..0..0. .0..1..0..1. .0..0..0..1. .0..1..0..1
%e ..0..1..1..0. .0..0..0..0. .0..0..1..0. .1..0..0..0. .0..1..1..0
%e ..1..1..0..1. .0..1..1..0. .0..0..0..1. .1..1..0..0. .1..0..1..1
%e ..1..0..0..1. .0..0..0..0. .1..0..0..1. .1..1..0..0. .0..1..1..1
%e ..1..0..0..0. .0..0..1..0. .1..0..0..0. .1..1..1..0. .1..0..0..1
%Y Column 1 is A000045(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 07 2018
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