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%I #4 Jan 30 2018 13:03:53
%S 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,3,2,2,3,0,0,5,3,4,3,5,0,0,8,5,6,6,5,
%T 8,0,0,13,8,11,10,11,8,13,0,0,21,13,18,22,22,18,13,21,0,0,34,21,31,47,
%U 102,47,31,21,34,0,0,55,34,53,143,390,390,143,53,34,55,0,0,89,55,91,418,1990
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0..0..0..0...0....0......0.......0........0..........0...........0
%C .0..1..1..2...3....5......8......13.......21.........34..........55
%C .0..1..1..2...3....5......8......13.......21.........34..........55
%C .0..2..2..4...6...11.....18......31.......53.........91.........156
%C .0..3..3..6..10...22.....47.....143......418.......1449........4821
%C .0..5..5.11..22..102....390....1990.....8875......42338......200422
%C .0..8..8.18..47..390...3101...21928...156972....1153968.....8497555
%C .0.13.13.31.143.1990..21928..300849..3354122...43052414...516822488
%C .0.21.21.53.418.8875.156972.3354122.54865647.1090267927.19403449274
%H R. H. Hardin, <a href="/A298957/b298957.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +a(n-2)
%F k=3: a(n) = a(n-1) +a(n-2)
%F k=4: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) -2*a(n-5) +a(n-6) +a(n-7)
%F k=5: [order 69]
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..1
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..1
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..1..1. .1..1..0..0
%e ..1..1..1..1. .0..0..0..0. .1..1..0..0. .1..1..1..1. .1..1..0..0
%e ..1..1..1..1. .0..0..0..0. .1..1..0..0. .1..1..1..1. .1..1..0..0
%Y Columns 2 and 3 are A000045(n-1).
%Y Column 4 is A298163.
%K nonn,tabl
%O 1,12
%A _R. H. Hardin_, Jan 30 2018
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