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%I A300314 #4 Mar 02 2018 17:59:12
%S A300314 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,73,45,45,73,32,64,157,148,
%T A300314 211,148,157,64,128,353,529,1537,1537,529,353,128,256,869,1747,8135,
%U A300314 15171,8135,1747,869,256,512,1993,5797,41485,120072,120072,41485,5797,1993,512
%N A300314 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
%C A300314 Table starts
%C A300314 ...1....2.....4.......8.......16.........32...........64............128
%C A300314 ...2....7....13......29.......73........157..........353............869
%C A300314 ...4...13....20......45......148........529.........1747...........5797
%C A300314 ...8...29....45.....211.....1537.......8135........41485.........237494
%C A300314 ..16...73...148....1537....15171.....120072......1008622........9188573
%C A300314 ..32..157...529....8135...120072....1676663.....23451403......352887797
%C A300314 ..64..353..1747...41485..1008622...23451403....543024998....13524308534
%C A300314 .128..869..5797..237494..9188573..352887797..13524308534...558233828840
%C A300314 .256.1993.19584.1335377.81099064.5253872974.332995274077.22733280314275
%H A300314 R. H. Hardin, <a href="/A300314/b300314.txt">Table of n, a(n) for n = 1..180</a>
%F A300314 Empirical for column k:
%F A300314 k=1: a(n) = 2*a(n-1)
%F A300314 k=2: a(n) = 4*a(n-1) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6
%F A300314 k=3: [order 16] for n>17
%F A300314 k=4: [order 55] for n>59
%e A300314 Some solutions for n=5 k=4
%e A300314 ..0..1..0..0. .0..0..0..1. .0..1..0..1. .0..1..0..0. .0..0..1..0
%e A300314 ..1..1..0..1. .1..0..0..0. .1..1..0..0. .1..1..0..1. .1..1..1..0
%e A300314 ..0..0..0..0. .1..1..0..0. .1..1..1..1. .1..1..1..1. .0..1..1..1
%e A300314 ..1..0..0..0. .1..1..0..0. .1..0..1..0. .1..1..1..1. .0..1..1..1
%e A300314 ..0..1..1..0. .0..1..0..1. .0..0..1..0. .0..1..1..0. .1..0..0..1
%Y A300314 Column 1 is A000079(n-1).
%Y A300314 Column 2 is A298215.
%K A300314 nonn,tabl
%O A300314 1,2
%A A300314 _R. H. Hardin_, Mar 02 2018

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