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Number of (n+2) X (7+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.
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%I #8 Dec 04 2018 11:04:15

%S 1200,1468,2404,3160,11456,19232,25280,91648,153856,202240,733184,

%T 1230848,1617920,5865472,9846784,12943360,46923776,78774272,103546880,

%U 375390208,630194176,828375040,3003121664,5041553408,6627000320

%N Number of (n+2) X (7+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 R. H. Hardin, <a href="/A252531/b252531.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-3) for n>5.

%F Empirical g.f.: 4*x*(300 + 367*x + 601*x^2 - 1610*x^3 - 72*x^4) / ((1 - 2*x)*(1 + 2*x + 4*x^2)). - _Colin Barker_, Dec 04 2018

%e Some solutions for n=4:

%e ..3..2..2..3..2..2..3..2..2....1..1..0..1..1..0..1..1..0

%e ..3..1..3..3..1..3..3..1..3....0..1..1..0..1..1..0..1..1

%e ..2..2..3..2..2..3..2..2..3....0..3..0..0..3..0..0..3..0

%e ..3..2..2..3..2..2..3..2..2....1..1..0..1..1..0..1..1..0

%e ..3..0..3..3..1..3..3..0..3....0..1..1..0..1..1..0..1..1

%e ..2..2..3..2..2..3..2..2..3....3..3..0..0..2..0..0..2..0

%Y Column 7 of A252532.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 18 2014