A009692 Number of partitions of {1, 2, ..., 2n} into pairs whose differences are primes.

1, 0, 1, 3, 10, 40, 153, 921, 5144, 30717, 230748, 1766056, 14052445, 116580521, 897876519, 7657321097, 75743979608, 788733735080, 7569825650083, 75242386295617, 831978453306391, 9444103049405370, 120064355466770831, 1579842230380587833

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• hard

Examples

			a(3) = 3: {{1,6}, {2,4}, {3,5}}, {{1,4}, {2,5}, {3,6}}, {{1,3}, {2,5}, {4,6}}. - _Alois P. Heinz_, Nov 15 2016
		

Crossrefs

Cf. A000341.

Programs

Maple

b:= proc(s) option remember; `if`(s={}, 1, (j-> add(`if`(i b({$1..2*n}):
seq(a(n), n=0..12);  # Alois P. Heinz, Nov 15 2016

Mathematica

b[s_] := b[s] = If[s == {}, 1, Function[j, Sum[If[i < j && PrimeQ[j - i], b[s ~Complement~ {i, j}], 0], {i, s}]][Max[s]]];
a[n_] := b[Range[2n]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 18}] (* Jean-François Alcover, Mar 01 2021, after Alois P. Heinz *)

Extensions

a(0), a(14)-a(18) from Alois P. Heinz, Nov 15 2016

a(19)-a(23) from Bert Dobbelaere, Feb 20 2020