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Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum one and no antidiagonal sum two.
1

%I #8 Dec 18 2018 09:25:37

%S 192,576,1632,4624,13328,38416,110544,318096,913680,2624400,7549200,

%T 21715600,62425360,179452816,515960336,1483482256,4265261840,

%U 12263347600,35258287120,101370918544,291456195856,837979129744,2409294812688

%N Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum one and no antidiagonal sum two.

%H R. H. Hardin, <a href="/A254847/b254847.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 8*a(n-3) + 12*a(n-4) + 20*a(n-5) + 32*a(n-6) - 64*a(n-8) - 64*a(n-9)

%F Empirical g.f.: 16*x*(12 + 24*x + 66*x^2 + 91*x^3 + 112*x^4 + 80*x^5 - 132*x^6 - 352*x^7 - 256*x^8) / ((1 + 2*x^2 - 4*x^3)*(1 + 2*x^2 + 4*x^3)*(1 - x - 4*x^2 - 4*x^3)). - _Colin Barker_, Dec 18 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 1 of A254854.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 08 2015