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%I #4 May 13 2018 10:41:48
%S 1,2,2,4,8,4,8,21,21,8,16,49,41,49,16,32,120,117,117,120,32,64,293,
%T 316,322,316,293,64,128,719,810,1100,1100,810,719,128,256,1774,2208,
%U 2957,5063,2957,2208,1774,256,512,4389,6012,8254,18879,18879,8254,6012,4389
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2.....4.....8......16.......32.......64.......128........256
%C ...2....8....21....49.....120......293......719......1774.......4389
%C ...4...21....41...117.....316......810.....2208......6012......15837
%C ...8...49...117...322....1100.....2957.....8254.....26698......77788
%C ..16..120...316..1100....5063....18879....68338....289227....1157258
%C ..32..293...810..2957...18879....89071...380640...2075796...10775870
%C ..64..719..2208..8254...68338...380640..1802240..12149499...76809028
%C .128.1774..6012.26698..289227..2075796.12149499.101407827..820468158
%C .256.4389.15837.77788.1157258.10775870.76809028.820468158.8813328376
%H R. H. Hardin, <a href="/A304472/b304472.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5
%F k=3: [order 10] for n>12
%F k=4: [order 21] for n>25
%F k=5: [order 84] for n>88
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..1..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
%e ..0..1..1..1. .1..0..1..1. .0..0..0..0. .0..0..1..0. .0..0..0..0
%e ..1..1..1..1. .1..1..1..1. .0..0..1..0. .0..0..0..1. .0..1..0..0
%e ..1..0..0..1. .1..0..1..1. .1..1..0..1. .0..0..1..0. .0..1..1..0
%e ..0..1..1..0. .0..0..1..1. .1..1..1..1. .1..0..0..1. .0..0..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A303721.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 13 2018
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