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

%I #8 Mar 20 2018 06:51:51

%S 1534,594,1260,1958,3530,6072,11762,21346,39202,80834,147842,276162,

%T 593666,1091074,2059522,4537346,8361986,15877122,35450882,65429506,

%U 124620802,280215554,517570562,987381762,2228158466,4117102594

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

%C Column 5 of A251894.

%H R. H. Hardin, <a href="/A251891/b251891.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 12*a(n-3) - 12*a(n-4) - 32*a(n-6) + 32*a(n-7) for n>12.

%F Empirical g.f.: 2*x*(767 - 470*x + 333*x^2 - 8855*x^3 + 6426*x^4 - 2725*x^5 + 23201*x^6 - 19680*x^7 + 4332*x^8 - 2156*x^9 + 1152*x^10 - 2304*x^11) / ((1 - x)*(1 - 2*x)*(1 + 2*x + 4*x^2)*(1 - 4*x^3)). - _Colin Barker_, Mar 20 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Cf. A251894.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2014