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%I #4 Jan 09 2018 07:37:05
%S 0,1,1,1,4,1,2,18,18,2,3,52,56,52,3,5,174,219,219,174,5,8,604,796,948,
%T 796,604,8,13,2048,3079,4258,4258,3079,2048,13,21,6948,11614,19561,
%U 23840,19561,11614,6948,21,34,23652,44076,88441,134642,134642,88441,44076
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 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.....56.....219......796......3079......11614.......44076.......167210
%C ..2....52....219.....948.....4258.....19561......88441......402245......1831311
%C ..3...174....796....4258....23840....134642.....750733.....4222383.....23711537
%C ..5...604...3079...19561...134642....938557....6423236....44289957....305715877
%C ..8..2048..11614...88441...750733...6423236...53630550...451993176...3822668362
%C .13..6948..44076..402245..4222383..44289957..451993176..4667940027..48407285130
%C .21.23652.167210.1831311.23711537.305715877.3822668362.48407285130.616122541550
%H R. H. Hardin, <a href="/A297951/b297951.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 20] for n>21
%F k=4: [order 66] for n>69
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..1..0..0. .0..1..1..1. .0..0..0..1. .0..1..0..0
%e ..0..1..1..1. .0..1..1..1. .0..1..0..0. .1..0..1..1. .1..0..1..1
%e ..1..1..0..1. .1..1..1..0. .0..1..0..1. .0..1..0..0. .1..1..0..0
%e ..0..0..0..1. .0..0..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..1
%e ..1..1..1..0. .1..1..1..1. .0..1..0..1. .0..1..0..1. .1..0..0..0
%Y Column 1 is A000045(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 09 2018
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