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%I #4 Feb 07 2018 09:57:54
%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,73,40,40,73,32,64,157,89,120,
%T 89,157,64,128,353,195,503,503,195,353,128,256,869,451,1492,2067,1492,
%U 451,869,256,512,1993,1046,4767,6605,6605,4767,1046,1993,512,1024,4557,2453
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2....4.....8.....16......32.......64.......128........256.........512
%C ...2....7...13....29.....73.....157......353.......869.......1993........4557
%C ...4...13...20....40.....89.....195......451......1046.......2453........5810
%C ...8...29...40...120....503....1492.....4767.....17127......56292......185937
%C ..16...73...89...503...2067....6605....30814....125890.....498977.....2155139
%C ..32..157..195..1492...6605...25754...150748....749550....3771027....20403891
%C ..64..353..451..4767..30814..150748..1262771...8560581...57300258...426035059
%C .128..869.1046.17127.125890..749550..8560581..72445170..624861384..6151095307
%C .256.1993.2453.56292.498977.3771027.57300258.624861384.7208056818.93531514754
%H R. H. Hardin, <a href="/A299350/b299350.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F 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 k=3: [order 14] for n>15
%F k=4: [order 62] for n>65
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..0..1. .0..1..0..1. .0..0..1..0. .0..0..0..1
%e ..0..0..1..0. .0..1..0..1. .0..0..1..1. .1..0..1..1. .1..1..1..0
%e ..1..1..1..0. .1..0..0..0. .0..0..1..1. .0..0..1..1. .0..1..1..1
%e ..0..1..1..1. .1..0..1..1. .1..0..1..0. .0..0..1..0. .0..1..0..0
%e ..0..1..0..0. .0..0..1..0. .1..0..0..0. .1..0..1..1. .1..0..1..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A298215.
%Y Column 3 is A298216.
%Y Column 4 is A298217.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 07 2018
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