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Number of (n+2) X (7+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 06:51:45

%S 2146,1182,2478,4490,11762,17774,33218,84866,142178,265730,678914,

%T 1137410,2125826,5431298,9099266,17006594,43450370,72794114,136052738,

%U 347602946,582352898,1088421890,2780823554,4658823170,8707375106

%N Number of (n+2) X (7+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 7 of A251894.

%H R. H. Hardin, <a href="/A251893/b251893.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 8*a(n-3) - 8*a(n-4) for n>9.

%F Empirical g.f.: 2*x*(1073 - 482*x + 648*x^2 - 7578*x^3 + 7492*x^4 - 2178*x^5 - 326*x^6 - 3264*x^7 + 4608*x^8) / ((1 - x)*(1 - 2*x)*(1 + 2*x + 4*x^2)). - _Colin Barker_, Mar 20 2018

%e Some solutions for n=4:

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

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

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

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

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

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

%Y Cf. A251894.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 10 2014