A067618 - OEIS

%I #8 Jun 24 2014 01:08:21

%S 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,

%T 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,

%U 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

%N Number of self-conjugate partitions of n into prime parts.

%t 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 *)

%Y Cf. A000700, A000701, A046682.

%K easy,nonn

%O 0,26

%A _Naohiro Nomoto_, Feb 01 2002

%E Edited by _Dean Hickerson_, Feb 11 2002