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%I #4 Jan 26 2018 08:30:34
%S 0,1,1,1,4,1,2,18,18,2,3,52,57,52,3,5,174,222,222,174,5,8,604,808,957,
%T 808,604,8,13,2048,3124,4288,4288,3124,2048,13,21,6948,11807,19722,
%U 23932,19722,11807,6948,21,34,23652,44846,89295,135243,135243,89295,44846
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3, 5 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.....957.....4288.....19722......89295......406426......1851746
%C ..3...174....808....4288....23932....135243.....754713.....4245549.....23848195
%C ..5...604...3124...19722...135243....942727....6456802....44530673....307427453
%C ..8..2048..11807...89295...754713...6456802...53950338...454801194...3847185453
%C .13..6948..44846..406426..4245549..44530673..454801194..4698205702..48730992802
%C .21.23652.170350.1851746.23848195.307427453.3847185453.48730992802.620363350692
%H R. H. Hardin, <a href="/A298770/b298770.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 66] for n>69
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e ..1..1..1..0. .1..1..1..1. .0..0..0..0. .1..1..1..1. .0..0..0..0
%e ..1..1..1..0. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1
%e ..1..1..1..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .1..1..1..1
%e ..1..1..1..0. .0..0..0..0. .0..0..0..1. .1..1..1..1. .1..1..1..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297945.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 26 2018
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