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Number of (6+2) X (n+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 3 5 6 or 7.
1

%I #8 Dec 03 2018 12:45:46

%S 904,764,984,1097,1667,2356,2769,4222,5992,7136,10911,15524,18561,

%T 28419,40483,48469,74254,105828,126768,194251,276904,331757,508407,

%U 724787,868425,1330878,1897360,2273440,3484135,4967196,5951817,9121435,13004131

%N Number of (6+2) X (n+2) 0..3 arrays with every 3 X 3 subblock row and diagonal sum equal to 0 3 5 6 or 7 and every 3 X 3 column and antidiagonal sum not equal to 0 3 5 6 or 7.

%H R. H. Hardin, <a href="/A252390/b252390.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-3) - 4*a(n-6) + a(n-9) for n>15.

%F Empirical g.f.: x*(904 + 764*x + 984*x^2 - 2519*x^3 - 1389*x^4 - 1580*x^5 + 1997*x^6 + 610*x^7 + 504*x^8 - 456*x^9 - 73*x^10 - 4*x^11 - 4*x^12 - 4*x^13 - x^14) / ((1 - x)*(1 + x + x^2)*(1 - 3*x^3 + x^6)). - _Colin Barker_, Dec 03 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

%Y Row 6 of A252384.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 17 2014