A134293 Number of ways to pair up {2..2n+1} so the sum of each pair is prime.

1, 1, 2, 6, 20, 60, 190, 764, 2337, 9812, 49538, 330058, 2133438, 11192143, 73469550, 462692414, 3692965270, 32635321384, 290171883863, 2572828730372, 22299380503953, 195129375058656, 1544534855847233, 13144353749969945, 128883813733449772, 1365629506139662111

Offset: 1

Author

T. D. Noe, Oct 17 2007

Keywords

• nonn

Comments

This sequence complements A000341, which is also related to A073364.

Examples

			a(3)=2 because for the set {2..7} there are two ways: {{2,3},{4,7},{5,6}} and {{2,5},{3,4},{6,7}}.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..35

Programs

Mathematica

a[n_] := Permanent[Array[Boole[PrimeQ[2 #1 + 2 #2 + 1]]&, {n, n}]];
Array[a, 15] (* Jean-François Alcover, Nov 03 2018 *)

PARI

a(n)={matpermanent(matrix(n,n,i,j,isprime(2*i + 2*j + 1)))} \\ Andrew Howroyd, Nov 03 2018

Formula

a(n) = permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0, depending on whether 2i+2j+1 is prime or composite, respectively.

Extensions

a(21)-a(26) from Andrew Howroyd, Nov 03 2018