%I #8 Dec 03 2018 15:35:31

%S 1051,903,1114,1361,2031,2778,3495,5195,7123,9045,13466,18506,23568,

%T 35117,48310,61587,91799,126339,161121,240194,330622,421704,628697,

%U 865442,1103919,1645811,2265619,2889981,4308650,5931330,7565952,11280053

%N Number of (7+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="/A252391/b252391.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>14.

%F Empirical g.f.: x*(1051 + 903*x + 1114*x^2 - 2843*x^3 - 1581*x^4 - 1678*x^5 + 2255*x^6 + 683*x^7 + 467*x^8 - 542*x^9 - 93*x^10 + 12*x^11 + 7*x^12 + 2*x^13) / ((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..0....3..1..2..0..1..2....3..2..1..3..2..1....3..0..0..0..0..3

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

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

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

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

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

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

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

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

%Y Row 7 of A252384.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 17 2014