The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A035363 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A035363

Number of partitions of n into even parts.
(history; published version)

#71 by Michael De Vlieger at Sat Sep 23 12:11:08 EDT 2023

STATUS

reviewed

approved

#70 by Joerg Arndt at Sat Sep 23 11:56:15 EDT 2023

STATUS

proposed

reviewed

#69 by Chai Wah Wu at Sat Sep 23 10:21:29 EDT 2023

STATUS

editing

proposed

#68 by Chai Wah Wu at Sat Sep 23 10:21:21 EDT 2023

PROG

(Python)

from sympy import npartitions

def A035363(n): return 0 if n&1 else npartitions(n>>1) # Chai Wah Wu, Sep 23 2023

STATUS

approved

editing

#67 by Alois P. Heinz at Tue Jun 22 20:00:28 EDT 2021

STATUS

editing

approved

#66 by Alois P. Heinz at Tue Jun 22 20:00:16 EDT 2021

MAPLE

# next Maple program:

a:= n-> `if`(n::odd, 0, combinat[numbpart](n/2)):

seq(a(n), n=0..84); # Alois P. Heinz, Jun 22 2021

STATUS

approved

editing

#65 by Susanna Cuyler at Mon May 24 00:12:07 EDT 2021

STATUS

proposed

approved

#64 by Gus Wiseman at Sun May 23 09:24:27 EDT 2021

STATUS

editing

proposed

#63 by Gus Wiseman at Sun May 23 09:23:47 EDT 2021

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], OddQ[Times@@(#+1)]&]], {n, 0, 30}] (* Gus Wiseman, May 22 2021 *)

CROSSREFS

A000041 also counts partitions whose sum is twice their length (A340387).

A016116 counts palindromic compositions.

A087897 counts partitions into odd parts > 1 (A341449).

A338911 lists products of pairs of primes both of even index.

Cf. A000041, A000290, A087897, A100484, A110618, A209816, A210249, A233771, A339004, A340385, A340387, A340786, A341447.

#62 by Gus Wiseman at Sun May 23 02:48:39 EDT 2021

CROSSREFS

The odd version for odd instead of even parts is A000009 (A066208).

The strict case (distinct parts) is A035457.

The multiplicative version for (factorizations ) is A340785.