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Number of (n+2) X 3 0..2 arrays with no 3 X 3 subblock having three equal diagonal elements or three equal antidiagonal elements, and new values 0..2 introduced in row major order.
1

%I #10 Jun 10 2018 20:47:26

%S 2592,55296,1180224,25190406,537665796,11475976536,244944162648,

%T 5228107832664,111589154041536,2381767878219264,50836645164242304,

%U 1085061443303739744,23159638720382882112,494321191641967752576

%N Number of (n+2) X 3 0..2 arrays with no 3 X 3 subblock having three equal diagonal elements or three equal antidiagonal elements, and new values 0..2 introduced in row major order.

%C Column 1 of A204782.

%H R. H. Hardin, <a href="/A204775/b204775.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 22*a(n-1) - 308*a(n-3) + 196*a(n-4).

%F Empirical g.f.: 54*x*(48 - 32*x - 672*x^2 + 441*x^3) / ((1 - 22*x + 14*x^2)*(1 - 14*x^2)). - _Colin Barker_, Jun 10 2018

%e Some solutions for n=3:

%e 0 0 0 0 0 1 0 1 1 0 1 2 0 0 1 0 0 0 0 1 0

%e 1 0 0 2 0 2 0 1 2 1 0 2 2 2 0 0 0 0 0 1 1

%e 2 1 1 2 2 1 2 1 2 2 0 1 0 0 2 1 1 2 1 0 2

%e 2 0 0 0 2 1 0 0 1 2 1 0 1 0 0 1 2 1 1 2 2

%e 1 2 2 2 0 1 0 2 0 2 2 2 0 2 2 0 2 1 0 1 1

%Y Cf. A204782.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 19 2012