A342139 Number of partitions of [2n] into pairs whose sums or differences are primes.

1, 1, 3, 8, 28, 167, 810, 4664, 38344, 207255, 2059900, 19385131, 174417011, 1922011637, 21058799803, 208257199434, 2905150193223, 38462668421772, 481607876817202, 7526871509864950

Offset: 0

Author

Alois P. Heinz, Mar 01 2021

Keywords

• nonn
• more

Examples

			a(2) = 3: {{1,4}, {2,3}}, {{1,3}, {2,4}}, {{1,2}, {3,4}}.
		

Links

• Wikipedia, Partition of a set

Crossrefs

Cf. A000341, A009692, A342136, A342155.

Programs

Maple

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

Mathematica

b[s_] := b[s] = If[s == {}, 1, With[{j = Max[s]}, Sum[If[i < j && AnyTrue[{j+i, j-i}, PrimeQ], b[s ~Complement~ {i, j}], 0], {i, s}]]];
a[n_] := b[Range[2n]];
a /@ Range[0, 15] (* Jean-François Alcover, Aug 25 2021, after Alois P. Heinz *)