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A298895 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%I A298895 #4 Jan 28 2018 09:07:58
%S A298895 0,0,0,0,1,0,0,3,3,0,0,2,1,2,0,0,11,4,4,11,0,0,13,4,11,4,13,0,0,34,11,
%T A298895 31,31,11,34,0,0,65,26,80,219,80,26,65,0,0,123,66,229,579,579,229,66,
%U A298895 123,0,0,266,171,681,1858,2963,1858,681,171,266,0,0,499,462,1969,8891,12224
%N A298895 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C A298895 Table starts
%C A298895 .0...0...0....0.....0......0.......0........0.........0..........0............0
%C A298895 .0...1...3....2....11.....13......34.......65.......123........266..........499
%C A298895 .0...3...1....4.....4.....11......26.......66.......171........462.........1248
%C A298895 .0...2...4...11....31.....80.....229......681......1969.......5973........18031
%C A298895 .0..11...4...31...219....579....1858.....8891.....34212.....128103.......538967
%C A298895 .0..13..11...80...579...2963...12224....72620....426475....2284203.....12768382
%C A298895 .0..34..26..229..1858..12224...74725...547497...4012035...28805843....209118279
%C A298895 .0..65..66..681..8891..72620..547497..5719782..54423404..502721390...4804572705
%C A298895 .0.123.171.1969.34212.426475.4012035.54423404.724538480.8857192378.112203393143
%H A298895 R. H. Hardin, <a href="/A298895/b298895.txt">Table of n, a(n) for n = 1..219</a>
%F A298895 Empirical for column k:
%F A298895 k=1: a(n) = a(n-1)
%F A298895 k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)
%F A298895 k=3: [order 17] for n>18
%F A298895 k=4: [order 58] for n>59
%e A298895 Some solutions for n=7 k=4
%e A298895 ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A298895 ..0..0..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A298895 ..1..1..1..1. .0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e A298895 ..1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1
%e A298895 ..0..0..0..0. .1..1..1..1. .0..0..0..0. .1..0..0..1. .1..0..0..1
%e A298895 ..0..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..0..1. .0..1..1..0
%e A298895 ..0..0..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1. .0..0..0..0
%Y A298895 Column 2 is A297870.
%K A298895 nonn,tabl
%O A298895 1,8
%A A298895 _R. H. Hardin_, Jan 28 2018