A052001 Even partition numbers.

2, 22, 30, 42, 56, 176, 490, 792, 1002, 1958, 2436, 3010, 3718, 5604, 6842, 12310, 37338, 53174, 89134, 105558, 124754, 204226, 451276, 614154, 715220, 831820, 1300156, 1741630, 2012558, 2323520, 4087968, 7089500, 8118264, 12132164

Offset

1,1

Comments

Intersection of A005843 and A000041; A059841(a(n)) * A167392(a(n)) = 1. - Reinhard Zumkeller, Nov 03 2009

Kolberg proves that this sequence is infinite. - Charles R Greathouse IV, Jan 23 2026

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

O. Kolberg, Note on the Parity of the Partition Functions, Mathematica Scandinavica, Volume 7 (1959), pp. 377-378.

Formula

a(n) = 2*A213179(n). - Omar E. Pol, May 08 2013

Mathematica

Select[PartitionsP[Range[100]], EvenQ] (* Jean-François Alcover, Mar 01 2019 *)

Prog

(PARI) for(n=1, 100, if((k=numbpart(n))%2==0, print1(k", "))) \\ Altug Alkan, Nov 02 2015
(Haskell)
a052001 n = a052001_list !! (n-1)
a052001_list = filter even a000041_list
-- Reinhard Zumkeller, Nov 03 2015

Crossrefs

Cf. A000041, A001560, A005843, A052002, A052003, A059841, A167392, A213179.

Sequence in context: A137106 A053962 A111771 * A275029 A085185 A166726

Adjacent sequences: A051998 A051999 A052000 * A052002 A052003 A052004

Keyword

nonn

Author

Patrick De Geest, Nov 15 1999

Extensions

Offset corrected by Reinhard Zumkeller, Nov 03 2015

Status

approved