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Number of (n+2) X (2+2) 0..3 arrays with every 3 X 3 subblock row and column sum nonprime and every diagonal and antidiagonal sum prime.
1

%I #6 Apr 21 2021 14:23:53

%S 981,508,828,1229,2672,5438,9647,22610,47398,86279,204832,432320,

%T 789967,1882338,3983708,7285937,17386988,36844782,67409449,160977268,

%U 341342946,624601177,1492090228,3164874902,5791630811,13837769762,29355806776

%N Number of (n+2) X (2+2) 0..3 arrays with every 3 X 3 subblock row and column sum nonprime and every diagonal and antidiagonal sum prime.

%C Column 2 of A251845.

%H R. H. Hardin, <a href="/A251839/b251839.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 17*a(n-3) -90*a(n-6) +191*a(n-9) -205*a(n-12) +128*a(n-15) -48*a(n-18) +8*a(n-21) for n > 26.

%e Some solutions for n=4

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

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

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

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

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

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

%Y Cf. A251845.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 09 2014