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A134293
Number of ways to pair up {2..2n+1} so the sum of each pair is prime.
2
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
1,3
COMMENTS
This sequence complements A000341, which is also related to A073364.
LINKS
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.
EXAMPLE
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}}.
MATHEMATICA
a[n_] := Permanent[Array[Boole[PrimeQ[2 #1 + 2 #2 + 1]]&, {n, n}]];
Array[a, 15] (* Jean-François Alcover, Nov 03 2018 *)
PROG
(PARI) a(n)={matpermanent(matrix(n, n, i, j, isprime(2*i + 2*j + 1)))} \\ Andrew Howroyd, Nov 03 2018
CROSSREFS
Sequence in context: A005628 A000620 A081251 * A363107 A136883 A289173
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 17 2007
EXTENSIONS
a(21)-a(26) from Andrew Howroyd, Nov 03 2018
STATUS
approved