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A303456 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A303456 #4 Apr 24 2018 10:22:23
%S A303456 1,2,2,4,8,4,8,32,32,8,16,128,232,128,16,32,512,1690,1696,512,32,64,
%T A303456 2048,12340,22756,12408,2048,64,128,8192,90112,306448,306767,90800,
%U A303456 8192,128,256,32768,658204,4129588,7626768,4136339,664512,32768,256,512,131072
%N A303456 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A303456 Table starts
%C A303456 ...1......2........4...........8............16..............32
%C A303456 ...2......8.......32.........128...........512............2048
%C A303456 ...4.....32......232........1690.........12340...........90112
%C A303456 ...8....128.....1696.......22756........306448.........4129588
%C A303456 ..16....512....12408......306767.......7626768.......189848373
%C A303456 ..32...2048....90800.....4136339.....189837638......8727953509
%C A303456 ..64...8192...664512....55781418....4726484016....401405461699
%C A303456 .128..32768..4863312...752277525..117683035940..18461936404456
%C A303456 .256.131072.35593024.10145443043.2930192820802.849140799884830
%H A303456 R. H. Hardin, <a href="/A303456/b303456.txt">Table of n, a(n) for n = 1..180</a>
%F A303456 Empirical for column k:
%F A303456 k=1: a(n) = 2*a(n-1)
%F A303456 k=2: a(n) = 4*a(n-1)
%F A303456 k=3: a(n) = 8*a(n-1) -4*a(n-2) -2*a(n-3) -36*a(n-4) -16*a(n-5)
%F A303456 k=4: [order 15]
%F A303456 k=5: [order 47]
%F A303456 Empirical for row n:
%F A303456 n=1: a(n) = 2*a(n-1)
%F A303456 n=2: a(n) = 4*a(n-1)
%F A303456 n=3: a(n) = 8*a(n-1) -40*a(n-3) +20*a(n-4) +8*a(n-5) -3*a(n-6) +32*a(n-7) for n>8
%F A303456 n=4: [order 15] for n>16
%F A303456 n=5: [order 68] for n>69
%e A303456 Some solutions for n=5 k=4
%e A303456 ..0..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..0..0. .0..0..0..1
%e A303456 ..1..1..1..0. .1..1..0..1. .0..1..0..1. .0..1..0..0. .0..0..1..0
%e A303456 ..0..0..1..1. .0..1..0..1. .1..0..0..0. .1..1..1..0. .0..0..1..1
%e A303456 ..0..1..1..0. .0..1..0..0. .1..1..1..1. .0..1..1..0. .0..0..0..1
%e A303456 ..0..0..0..1. .0..0..1..1. .1..1..0..1. .0..0..1..1. .0..0..1..0
%Y A303456 Column 1 is A000079(n-1).
%Y A303456 Column 2 is A004171(n-1).
%Y A303456 Row 1 is A000079(n-1).
%Y A303456 Row 2 is A004171(n-1).
%K A303456 nonn,tabl
%O A303456 1,2
%A A303456 _R. H. Hardin_, Apr 24 2018