A240573 Number of partitions of n such that the number of even parts is a part.

0, 0, 0, 1, 2, 3, 5, 7, 10, 15, 21, 28, 38, 51, 67, 89, 116, 149, 192, 245, 310, 393, 494, 617, 770, 956, 1181, 1457, 1790, 2190, 2675, 3257, 3952, 4788, 5784, 6968, 8380, 10053, 12032, 14378, 17144, 20400, 24236, 28740, 34018, 40208, 47443, 55887, 65744

Offset

0,5

Links

Table of n, a(n) for n=0..48.

Example

a(10) counts these 21 partitions:  82, 811, 721, 631, 6211, 61111, 541, 5221, 52111, 4321, 43111, 4222, 421111, 4111111, 3322, 33211, 32221, 322111, 3211111, 22111111, 211111111.

Mathematica

z = 62; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Count[Mod[p, 2], 0]]], {n, 0, z}]

Crossrefs

Cf. A240574, A240575, A240576, A240577, A240578, A240579.

Sequence in context: A338553 A272402 A321176 * A160571 A238543 A184641

Adjacent sequences: A240570 A240571 A240572 * A240574 A240575 A240576

Keyword

nonn,easy

Author

Clark Kimberling, Apr 10 2014

Status

approved