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%I #4 Jun 30 2018 19:19:11
%S 0,1,1,1,7,1,2,23,23,2,3,86,83,86,3,5,313,464,464,313,5,8,1145,2280,
%T 3909,2280,1145,8,13,4184,11423,29877,29877,11423,4184,13,21,15293,
%U 57453,228485,353009,228485,57453,15293,21,34,55895,288496,1755475,4067961
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1.......1.........2..........3............5..............8
%C ..1.....7......23........86........313.........1145...........4184
%C ..1....23......83.......464.......2280........11423..........57453
%C ..2....86.....464......3909......29877.......228485........1755475
%C ..3...313....2280.....29877.....353009......4067961.......47958446
%C ..5..1145...11423....228485....4067961.....70282175.....1244767536
%C ..8..4184...57453...1755475...47958446...1244767536....33482107028
%C .13.15293..288496..13526926..564507777..22077180053...901574650029
%C .21.55895.1447883.103864609.6610746658.388558892008.24039453398630
%H R. H. Hardin, <a href="/A316383/b316383.txt">Table of n, a(n) for n = 1..180</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 15] for n>16
%F k=4: [order 50] for n>51
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..1..0. .0..1..0..0. .0..0..1..1. .0..1..0..1
%e ..1..1..1..1. .0..1..1..0. .0..0..1..0. .1..0..0..1. .1..0..0..1
%e ..1..1..0..1. .1..0..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1
%e ..0..1..0..0. .0..0..0..1. .1..0..0..1. .0..1..1..0. .0..0..0..0
%e ..0..0..0..1. .1..0..1..0. .1..1..0..1. .1..0..0..0. .0..1..1..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A303890.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jun 30 2018
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