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%I #4 Feb 12 2018 20:39:54
%S 0,1,1,1,4,1,2,18,18,2,3,52,57,52,3,5,174,222,222,174,5,8,604,808,965,
%T 808,604,8,13,2048,3124,4342,4342,3124,2048,13,21,6948,11807,20044,
%U 24588,20044,11807,6948,21,34,23652,44846,91193,140401,140401,91193,44846
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1......1.......2........3.........5..........8..........13...........21
%C ..1.....4.....18......52......174.......604.......2048........6948........23652
%C ..1....18.....57.....222......808......3124......11807.......44846.......170350
%C ..2....52....222.....965.....4342.....20044......91193......417122......1909312
%C ..3...174....808....4342....24588....140401.....792454.....4505710.....25597272
%C ..5...604...3124...20044...140401....997212....6974944....49037025....345316723
%C ..8..2048..11807...91193...792454...6974944...60087975...521019836...4532637754
%C .13..6948..44846..417122..4505710..49037025..521019836..5576669621..59935963606
%C .21.23652.170350.1909312.25597272.345316723.4532637754.59935963606.796438022548
%H R. H. Hardin, <a href="/A299567/b299567.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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 19] for n>20
%F k=4: [order 67] for n>70
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
%e ..0..0..0..1. .0..0..0..0. .0..0..0..1. .1..1..1..1. .0..0..0..1
%e ..0..0..0..1. .0..0..0..0. .0..0..0..1. .1..1..1..1. .0..0..0..1
%e ..0..0..1..0. .0..0..0..0. .0..0..0..1. .1..1..1..1. .1..1..1..1
%e ..1..1..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .1..0..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297945.
%Y Column 3 is A298765.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 12 2018
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