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Number of (n+1)X8 0..1 arrays with the number of rightwards and downwards edge increases in each 2X2 subblock differing from the number in all its horizontal and vertical neighbors
1

%I #5 Mar 31 2012 12:37:04

%S 3516,638,850,1192,1852,2752,4480,6208,9168,12480,18688,25664,38832,

%T 53952,82224,114112,173736,240704,366080,507072,771160,1068096,

%U 1624720,2250304,3423744,4741312,7214768,9989696,15203384,21047488,32037296

%N Number of (n+1)X8 0..1 arrays with the number of rightwards and downwards edge increases in each 2X2 subblock differing from the number in all its horizontal and vertical neighbors

%C Column 7 of A205072

%H R. H. Hardin, <a href="/A205071/b205071.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-2) -2*a(n-6) -3*a(n-8) -3*a(n-10) -2*a(n-12) +4*a(n-16) +6*a(n-18) +14*a(n-20) +20*a(n-22) +24*a(n-24) +26*a(n-26) +26*a(n-28) +24*a(n-30) +21*a(n-32) +15*a(n-34) +10*a(n-36) +6*a(n-38) +3*a(n-40) +a(n-42) for n>48

%e Some solutions for n=4

%e ..0..1..0..1..0..0..0..1....1..0..0..1..0..0..0..0....1..1..1..0..0..0..0..0

%e ..0..0..0..0..1..0..0..0....0..1..0..1..1..1..0..1....0..1..1..1..1..0..1..0

%e ..0..1..0..0..0..1..0..1....0..0..0..0..0..1..0..0....1..0..1..0..1..0..0..0

%e ..0..0..1..0..0..0..0..0....0..1..0..1..0..1..1..1....1..1..1..1..1..1..1..0

%e ..0..0..0..1..0..1..0..1....0..0..0..0..0..0..0..1....0..0..1..0..1..0..1..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 21 2012