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A252252 Number of (n+2) X (6+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

%S 616,359,318,336,366,405,453,531,633,759,963,1230,1560,2094,2793,3657,

%T 5055,6885,9147,12807,17598,23520,33102,45645,61149,86235,119073,

%U 159663,225339,311310,417576,589518,814593,1092801,1542951,2132205,2860563

%N Number of (n+2) X (6+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="/A252252/b252252.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*(616 - 257*x - 41*x^2 - 1830*x^3 + 801*x^4 + 162*x^5 + 610*x^6 - 269*x^7 - 56*x^8) / ((1 - x)*(1 - 3*x^3 + x^6)). - _Colin Barker_, Dec 03 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Column 6 of A252254.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 16 2014

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Last modified October 18 14:14 EDT 2021. Contains 348068 sequences. (Running on oeis4.)