A052001 - OEIS

%I #31 Jan 28 2026 16:41:00

%S 2,22,30,42,56,176,490,792,1002,1958,2436,3010,3718,5604,6842,12310,

%T 37338,53174,89134,105558,124754,204226,451276,614154,715220,831820,

%U 1300156,1741630,2012558,2323520,4087968,7089500,8118264,12132164

%N Even partition numbers.

%C Intersection of A005843 and A000041; A059841(a(n)) * A167392(a(n)) = 1. - _Reinhard Zumkeller_, Nov 03 2009

%C Kolberg proves that this sequence is infinite. - _Charles R Greathouse IV_, Jan 23 2026

%H Reinhard Zumkeller, <a href="/A052001/b052001.txt">Table of n, a(n) for n = 1..1000</a>

%H O. Kolberg, <a href="http://dml.mathdoc.fr/item/GDZPPN00234601X/">Note on the Parity of the Partition Functions</a>, Mathematica Scandinavica, Volume 7 (1959), pp. 377-378.

%F a(n) = 2*A213179(n). - _Omar E. Pol_, May 08 2013

%t Select[PartitionsP[Range[100]], EvenQ] (* _Jean-François Alcover_, Mar 01 2019 *)

%o (PARI) for(n=1, 100, if((k=numbpart(n))%2==0, print1(k", "))) \\ _Altug Alkan_, Nov 02 2015

%o (Haskell)

%o a052001 n = a052001_list !! (n-1)

%o a052001_list = filter even a000041_list

%o -- _Reinhard Zumkeller_, Nov 03 2015

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

%K nonn

%O 1,1

%A _Patrick De Geest_, Nov 15 1999

%E Offset corrected by _Reinhard Zumkeller_, Nov 03 2015