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A067618 Number of self-conjugate partitions of n into prime parts. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,26

LINKS

Table of n, a(n) for n=0..102.

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 *)

CROSSREFS

Cf. A000700, A000701, A046682.

Sequence in context: A056170 A248395 A059483 * A279255 A055029 A126812

Adjacent sequences:  A067615 A067616 A067617 * A067619 A067620 A067621

KEYWORD

easy,nonn

AUTHOR

Naohiro Nomoto, Feb 01 2002

EXTENSIONS

Edited by Dean Hickerson, Feb 11 2002

STATUS

approved

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Last modified August 2 02:53 EDT 2021. Contains 346409 sequences. (Running on oeis4.)