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%I #4 Jun 26 2018 17:42:55
%S 1,2,2,4,8,4,8,23,23,8,16,65,78,65,16,32,192,271,271,192,32,64,569,
%T 982,1253,982,569,64,128,1709,3619,5925,5925,3619,1709,128,256,5162,
%U 13454,28597,36585,28597,13454,5162,256,512,15663,50193,139490,232633,232633
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1.....2......4.......8.......16.........32..........64..........128
%C ...2.....8.....23......65......192........569........1709.........5162
%C ...4....23.....78.....271......982.......3619.......13454........50193
%C ...8....65....271....1253.....5925......28597......139490.......684312
%C ..16...192....982....5925....36585.....232633.....1494780......9661315
%C ..32...569...3619...28597...232633....1962143....16731864....143845449
%C ..64..1709..13454..139490..1494780...16731864...189577494...2170853960
%C .128..5162..50193..684312..9661315..143845449..2170853960..33224254530
%C .256.15663.187620.3366213.62645367.1242037097.24994758941.512094847931
%H R. H. Hardin, <a href="/A316209/b316209.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +3*a(n-2) -6*a(n-3) -8*a(n-4) for n>5
%F k=3: [order 16]
%F k=4: [order 57] for n>59
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..1..1. .0..1..1..1
%e ..1..1..1..1. .1..1..0..1. .1..1..1..1. .1..0..1..1. .1..1..1..1
%e ..0..1..1..0. .0..0..0..1. .1..0..1..0. .0..1..0..1. .1..1..1..0
%e ..1..1..0..0. .0..0..1..1. .1..1..1..1. .0..1..0..0. .0..1..0..0
%e ..1..1..1..0. .1..0..0..1. .1..0..1..1. .1..0..1..1. .1..1..0..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A304304.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jun 26 2018
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