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%I #4 Mar 12 2018 11:29:38
%S 0,0,0,0,1,0,0,2,2,0,0,4,3,4,0,0,9,11,11,9,0,0,19,32,36,32,19,0,0,41,
%T 102,179,179,102,41,0,0,88,330,735,1536,735,330,88,0,0,189,1059,3482,
%U 10374,10374,3482,1059,189,0,0,406,3418,15986,78932,116954,78932,15986,3418
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .0...0....0.....0.......0.........0...........0............0..............0
%C .0...1....2.....4.......9........19..........41...........88............189
%C .0...2....3....11......32.......102.........330.........1059...........3418
%C .0...4...11....36.....179.......735........3482........15986..........74347
%C .0...9...32...179....1536.....10374.......78932.......592064........4449947
%C .0..19..102...735...10374....116954.....1413931.....17336190......210669938
%C .0..41..330..3482...78932...1413931....27354464....538564737....10457318118
%C .0..88.1059.15986..592064..17336190...538564737..16992197390...534677180915
%C .0.189.3418.74347.4449947.210669938.10457318118.534677180915.27071152148341
%H R. H. Hardin, <a href="/A300776/b300776.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)
%F k=3: [order 15]
%F k=4: [order 56] for n>57
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..1..1
%e ..0..0..1..1. .0..1..1..1. .0..1..1..1. .0..1..1..0. .0..1..1..1
%e ..0..0..1..0. .1..0..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..0
%e ..1..1..0..0. .1..0..0..1. .0..0..0..1. .0..0..1..1. .0..0..0..0
%e ..1..0..0..0. .1..1..1..1. .0..0..1..1. .0..1..1..1. .0..0..0..0
%Y Column 2 is A078039(n-2).
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Mar 12 2018
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