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A299661 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

%I A299661 #4 Feb 15 2018 14:49:03
%S A299661 1,2,2,4,8,4,8,32,32,8,16,128,227,128,16,32,512,1642,1642,512,32,64,
%T A299661 2048,11888,22087,11888,2048,64,128,8192,86123,297071,297071,86123,
%U A299661 8192,128,256,32768,624007,4001253,7411398,4001253,624007,32768,256,512,131072
%N A299661 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
%C A299661 Table starts
%C A299661 ...1......2........4..........8............16..............32
%C A299661 ...2......8.......32........128...........512............2048
%C A299661 ...4.....32......227.......1642.........11888...........86123
%C A299661 ...8....128.....1642......22087........297071.........4001253
%C A299661 ..16....512....11888.....297071.......7411398.......185302633
%C A299661 ..32...2048....86123....4001253.....185302633......8607101770
%C A299661 ..64...8192...624007...53909088....4634931975....400012077773
%C A299661 .128..32768..4521433..726363190..115940148451..18591844096646
%C A299661 .256.131072.32761769.9787119222.2900256951630.864147943636240
%H A299661 R. H. Hardin, <a href="/A299661/b299661.txt">Table of n, a(n) for n = 1..180</a>
%F A299661 Empirical for column k:
%F A299661 k=1: a(n) = 2*a(n-1)
%F A299661 k=2: a(n) = 4*a(n-1)
%F A299661 k=3: [order 8]
%F A299661 k=4: [order 24]
%F A299661 k=5: [order 89]
%e A299661 Some solutions for n=5 k=5
%e A299661 ..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0
%e A299661 ..0..0..0..0..0. .0..0..1..1..0. .0..0..1..1..0. .0..1..0..0..0
%e A299661 ..1..0..0..1..0. .1..1..1..1..0. .0..0..0..1..0. .0..0..1..1..1
%e A299661 ..1..1..0..1..0. .1..1..0..0..0. .0..1..1..1..1. .0..1..1..0..0
%e A299661 ..1..1..0..1..1. .0..0..0..1..0. .0..0..0..1..0. .0..0..1..1..1
%Y A299661 Column 1 is A000079(n-1).
%Y A299661 Column 2 is A004171(n-1).
%K A299661 nonn,tabl
%O A299661 1,2
%A A299661 _R. H. Hardin_, Feb 15 2018