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A252538 Number of (6+2) X (n+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

%I A252538 #7 Dec 04 2018 14:37:24
%S A252538 649,964,1748,2504,7136,13184,19232,54656,102272,150656,427520,805376,
%T A252538 1192448,3381248,6391808,9488384,26894336,50929664,75702272,214532096,
%U A252538 406618112,604798976,1713766400,3249668096,4835115008,13700169728
%N A252538 Number of (6+2) X (n+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 2 3 6 or 7.
%H A252538 R. H. Hardin, <a href="/A252538/b252538.txt">Table of n, a(n) for n = 1..210</a>
%F A252538 Empirical: a(n) = 12*a(n-3) - 32*a(n-6) for n>8.
%F A252538 Empirical g.f.: x*(649 + 964*x + 1748*x^2 - 5284*x^3 - 4432*x^4 - 7792*x^5 + 9952*x^6 - 128*x^7) / ((1 - 2*x)*(1 + 2*x + 4*x^2)*(1 - 4*x^3)). - _Colin Barker_, Dec 04 2018
%e A252538 Some solutions for n=4:
%e A252538 ..3..1..3..3..1..3....0..0..2..0..0..2....1..3..3..0..3..3....1..0..1..1..0..1
%e A252538 ..2..2..3..2..2..3....0..1..1..0..1..1....2..3..2..2..3..2....0..0..3..0..0..2
%e A252538 ..3..2..2..3..2..2....1..0..1..1..0..1....2..2..3..2..2..3....0..1..1..0..1..1
%e A252538 ..3..1..3..3..1..3....0..0..3..0..0..3....1..3..3..0..3..3....1..0..1..1..0..1
%e A252538 ..2..2..3..2..2..3....0..1..1..0..1..1....2..3..2..2..3..2....0..0..2..0..0..3
%e A252538 ..3..2..2..3..2..2....1..0..1..1..0..1....2..2..3..2..2..3....0..1..1..0..1..1
%e A252538 ..0..0..3..3..1..3....3..0..3..0..0..2....0..3..3..1..3..3....1..0..1..1..0..1
%e A252538 ..2..2..3..2..2..3....0..1..1..0..1..2....2..3..2..2..3..2....3..0..3..0..0..3
%Y A252538 Row 6 of A252532.
%K A252538 nonn
%O A252538 1,1
%A A252538 _R. H. Hardin_, Dec 18 2014