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A299654 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

%I A299654 #4 Feb 15 2018 14:43:08
%S A299654 1,2,2,4,8,4,8,32,32,8,16,128,247,128,16,32,512,1924,1924,512,32,64,
%T A299654 2048,14981,29408,14981,2048,64,128,8192,116654,448993,448993,116654,
%U A299654 8192,128,256,32768,908360,6856789,13431706,6856789,908360,32768,256,512,131072
%N A299654 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
%C A299654 Table starts
%C A299654 ...1......2........4...........8.............16...............32
%C A299654 ...2......8.......32.........128............512.............2048
%C A299654 ...4.....32......247........1924..........14981...........116654
%C A299654 ...8....128.....1924.......29408.........448993..........6856789
%C A299654 ..16....512....14981......448993.......13431706........401989538
%C A299654 ..32...2048...116654.....6856789......401989538......23582064542
%C A299654 ..64...8192...908360...104711327....12030404350....1383316377321
%C A299654 .128..32768..7073213..1599074414...360039414559...81146123707386
%C A299654 .256.131072.55077652.24419877459.10775053220325.4760069868306954
%H A299654 R. H. Hardin, <a href="/A299654/b299654.txt">Table of n, a(n) for n = 1..241</a>
%F A299654 Empirical for column k:
%F A299654 k=1: a(n) = 2*a(n-1)
%F A299654 k=2: a(n) = 4*a(n-1)
%F A299654 k=3: a(n) = 7*a(n-1) +5*a(n-2) +9*a(n-3) -a(n-4) -6*a(n-5)
%F A299654 k=4: [order 14]
%F A299654 k=5: [order 31]
%F A299654 k=6: [order 89]
%e A299654 Some solutions for n=5 k=4
%e A299654 ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1
%e A299654 ..0..1..1..1. .0..0..0..1. .1..0..0..0. .1..0..0..1. .0..0..1..0
%e A299654 ..1..0..0..1. .0..1..1..0. .0..1..1..1. .1..1..0..0. .0..1..1..1
%e A299654 ..1..0..1..0. .1..1..1..0. .0..0..0..0. .1..0..1..0. .1..0..0..1
%e A299654 ..0..1..1..1. .1..0..1..0. .0..0..1..0. .0..0..0..0. .1..1..0..0
%Y A299654 Column 1 is A000079(n-1).
%Y A299654 Column 2 is A004171(n-1).
%K A299654 nonn,tabl
%O A299654 1,2
%A A299654 _R. H. Hardin_, Feb 15 2018