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%I A299814 #4 Feb 19 2018 15:38:19
%S A299814 1,2,2,3,4,3,5,4,4,5,8,16,12,16,8,13,50,43,43,50,13,21,112,91,476,91,
%T A299814 112,21,34,348,519,1739,1739,519,348,34,55,1028,1721,11312,11460,
%U A299814 11312,1721,1028,55,89,2796,5886,80892,91721,91721,80892,5886,2796,89,144,8216
%N A299814 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C A299814 Table starts
%C A299814 ..1....2.....3.......5........8.........13...........21.............34
%C A299814 ..2....4.....4......16.......50........112..........348...........1028
%C A299814 ..3....4....12......43.......91........519.........1721...........5886
%C A299814 ..5...16....43.....476.....1739......11312........80892.........470799
%C A299814 ..8...50....91....1739....11460......91721......1087487.......10193140
%C A299814 .13..112...519...11312....91721....1881856.....32361748......503025918
%C A299814 .21..348..1721...80892..1087487...32361748...1009387819....26528688317
%C A299814 .34.1028..5886..470799.10193140..503025918..26528688317..1201130067486
%C A299814 .55.2796.24858.3083661.99383076.9210499641.792668582776.60813283508109
%H A299814 R. H. Hardin, <a href="/A299814/b299814.txt">Table of n, a(n) for n = 1..180</a>
%F A299814 Empirical for column k:
%F A299814 k=1: a(n) = a(n-1) +a(n-2)
%F A299814 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 A299814 k=3: [order 17] for n>18
%F A299814 k=4: [order 55] for n>58
%e A299814 Some solutions for n=5 k=4
%e A299814 ..0..1..1..1. .0..0..0..1. .0..1..1..1. .0..1..0..0. .0..1..1..1
%e A299814 ..0..1..1..1. .0..0..0..1. .0..1..1..1. .1..1..1..1. .1..1..0..0
%e A299814 ..1..1..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1
%e A299814 ..1..1..0..0. .1..1..0..0. .1..0..0..0. .1..1..1..1. .0..1..1..1
%e A299814 ..0..0..0..0. .1..1..1..1. .1..0..0..0. .1..1..1..1. .0..1..1..1
%Y A299814 Column 1 is A000045(n+1).
%Y A299814 Column 2 is A298148.
%K A299814 nonn,tabl
%O A299814 1,2
%A A299814 _R. H. Hardin_, Feb 19 2018

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