A067618 Number of self-conjugate partitions of n into prime parts.

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 1, 4, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 1, 3, 0, 0, 0, 5, 0, 0, 1, 6, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 1, 5, 0, 0, 0, 7, 0, 0, 0, 9, 0, 0, 0, 5, 0

Offset: 0

Author

Naohiro Nomoto, Feb 01 2002

Keywords

• easy
• nonn

Crossrefs

Cf. A000700, A000701, A046682.

Programs

Mathematica

f[0, m_, k_] := 1; f[n_, 0, k_] := If[n==0, 1, 0]; f[n_, m_, k_] := If[n<0||m<0, 0, Module[{r}, f[n, m, k]=f[n, m-1, k]+If[PrimeQ[m+k], Sum[If[PrimeQ[r+k], f[n-r(2m-r), m-r-1, k+r], 0], {r, 1, m}], 0]]]; a[n_] := f[n, Floor[n/4]+1, 0]; (* f[n, m, k] = number of self-conjugate partitions of n with parts <= m such that every part+k is prime *)

Extensions

Edited by Dean Hickerson, Feb 11 2002