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Number of (7+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.
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%I #8 Dec 05 2018 06:13:46

%S 823,1344,2332,3160,10720,18656,25280,85760,149248,202240,686080,

%T 1193984,1617920,5488640,9551872,12943360,43909120,76414976,103546880,

%U 351272960,611319808,828375040,2810183680,4890558464,6627000320,22481469440

%N Number of (7+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 R. H. Hardin, <a href="/A252539/b252539.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.: x*(823 + 1344*x + 2332*x^2 - 3424*x^3 - 32*x^4) / ((1 - 2*x)*(1 + 2*x + 4*x^2)). - _Colin Barker_, Dec 05 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

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

%Y Row 7 of A252532.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 18 2014