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A283635 Number of 2 X n 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly two elements. 1

%I #7 Feb 21 2019 09:49:15

%S 0,0,0,36,88,516,2076,7372,27108,92436,308980,1013112,3250572,

%T 10288376,32139960,99287748,303857760,922134588,2777950524,8314125460,

%U 24737931132,73218906420,215681560092,632587894224,1848037669164,5379301732896

%N Number of 2 X n 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly two elements.

%H R. H. Hardin, <a href="/A283635/b283635.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 5*a(n-3) - 42*a(n-4) - 33*a(n-5) + 51*a(n-6) + 156*a(n-7) + 144*a(n-8) + 64*a(n-9).

%F Empirical g.f.: 4*x^4*(9 - 5*x + 9*x^2 + 45*x^3) / (1 - x - 3*x^2 - 4*x^3)^3. - _Colin Barker_, Feb 21 2019

%e Some solutions for n=4:

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

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

%Y Row 2 of A283634.

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 12 2017

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