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%I #4 Mar 02 2018 18:06:44
%S 1,2,2,3,4,3,5,4,4,5,8,16,16,16,8,13,50,61,61,50,13,21,112,186,735,
%T 186,112,21,34,348,977,3486,3486,977,348,34,55,1028,3875,25797,31345,
%U 25797,3875,1028,55,89,2796,15976,203113,345605,345605,203113,15976,2796,89
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1....2.....3........5.........8..........13............21...............34
%C ..2....4.....4.......16........50.........112...........348.............1028
%C ..3....4....16.......61.......186.........977..........3875............15976
%C ..5...16....61......735......3486.......25797........203113..........1378779
%C ..8...50...186.....3486.....31345......345605.......4705725.........55447293
%C .13..112...977....25797....345605.....8002885.....178277369.......3616312721
%C .21..348..3875...203113...4705725...178277369....7221094975.....257924884697
%C .34.1028.15976..1378779..55447293..3616312721..257924884697...16292595627604
%C .55.2796.69695.10140973.678378012.80381600442.9967764866344.1108503299923830
%H R. H. Hardin, <a href="/A300321/b300321.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) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 15] for n>17
%F k=4: [order 40] for n>43
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..0. .0..0..1..1
%e ..1..0..0..0. .1..0..0..0. .1..1..0..0. .1..1..1..1. .0..0..0..0
%e ..1..1..0..0. .1..1..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1
%e ..1..1..1..0. .1..1..1..1. .1..1..0..0. .1..1..1..1. .1..0..1..1
%e ..1..1..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..0. .1..0..1..1
%Y Column 1 is A000045(n+1).
%Y Column 2 is A298148.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 02 2018
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