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%I #4 Jun 23 2018 12:46:32
%S 1,2,2,4,4,4,8,5,5,8,16,9,17,9,16,32,22,32,32,22,32,64,45,77,103,77,
%T 45,64,128,101,207,298,298,207,101,128,256,218,523,962,1188,962,523,
%U 218,256,512,477,1304,2966,4849,4849,2966,1304,477,512,1024,1041,3307,8756,19176
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 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...4....5.....9.....22......45......101.......218........477........1041
%C ...4...5...17....32.....77.....207......523......1304.......3307........8414
%C ...8...9...32...103....298.....962.....2966......8756......26287.......79873
%C ..16..22...77...298...1188....4849....19176.....75681.....302442.....1206813
%C ..32..45..207...962...4849...25226...128710....660871....3402775....17536734
%C ..64.101..523..2966..19176..128710...842280...5553315...36528087...240890311
%C .128.218.1304..8756..75681..660871..5553315..47632142..405555135..3465256979
%C .256.477.3307.26287.302442.3402775.36528087.405555135.4469582265.49440451905
%H R. H. Hardin, <a href="/A306166/b306166.txt">Table of n, a(n) for n = 1..287</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6
%F k=3: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -8*a(n-6) -8*a(n-7) for n>10
%F k=4: [order 18] for n>23
%F k=5: [order 40] for n>47
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..1
%e ..1..0..0..0. .0..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..1..1
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1
%e ..1..0..0..0. .1..0..1..0. .0..0..0..0. .1..0..0..0. .1..1..1..1
%e ..0..0..0..0. .0..0..0..1. .0..1..0..0. .0..0..0..0. .1..0..1..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A052962 for n>2.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jun 23 2018
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