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A252250 Number of (n+2) X (4+2) 0..3 arrays with every 3 X 3 subblock row and column sum not equal to 0 3 5 6 or 7 and every 3 X 3 diagonal and antidiagonal sum equal to 0 3 5 6 or 7. 1

%I #7 Dec 02 2018 14:26:22

%S 352,268,249,267,297,336,384,462,564,690,894,1161,1491,2025,2724,3588,

%T 4986,6816,9078,12738,17529,23451,33033,45576,61080,86166,119004,

%U 159594,225270,311241,417507,589449,814524,1092732,1542882,2132136,2860494

%N Number of (n+2) X (4+2) 0..3 arrays with every 3 X 3 subblock row and column sum not equal to 0 3 5 6 or 7 and every 3 X 3 diagonal and antidiagonal sum equal to 0 3 5 6 or 7.

%H R. H. Hardin, <a href="/A252250/b252250.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 3*a(n-3) - 3*a(n-4) - a(n-6) + a(n-7) for n>9.

%F Empirical g.f.: x*(352 - 84*x - 19*x^2 - 1038*x^3 + 282*x^4 + 96*x^5 + 346*x^6 - 96*x^7 - 34*x^8) / ((1 - x)*(1 - 3*x^3 + x^6)). - _Colin Barker_, Dec 02 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 4 of A252254.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2014

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