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Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock summing to a prime.
1

%I #9 Nov 30 2018 10:04:51

%S 114,856,6398,47874,358070,2679006,20039054,149921686,1121458998,

%T 8389937086,62760664590,469520691478,3512289126086,26275557518190,

%U 196558587418526,1470448905636774,11000011255301078,82290268441602622

%N Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock summing to a prime.

%H R. H. Hardin, <a href="/A251452/b251452.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 55*a(n-2) - 46*a(n-3) - 470*a(n-4) + 76*a(n-5) + 1092*a(n-6) + 432*a(n-7).

%F Empirical g.f.: 2*x*(57 + 314*x - 792*x^2 - 3379*x^3 + 1694*x^4 + 8880*x^5 + 3456*x^6) / (1 - 2*x - 55*x^2 + 46*x^3 + 470*x^4 - 76*x^5 - 1092*x^6 - 432*x^7). - _Colin Barker_, Nov 29 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A251459.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 02 2014