A337585 a(n) is the number of integer multisets (partitions) for which the number of partitions of n with matching multiplicity multiset is odd.

1, 1, 2, 3, 5, 3, 9, 9, 14, 14, 18, 22, 31, 27, 37, 42, 65, 61, 83, 82, 111, 110, 142, 147, 187, 190, 230, 242, 296, 319, 358, 412, 471, 505, 600, 595, 753, 781, 895, 921, 1082, 1143, 1272, 1405, 1587, 1632, 1872, 2000, 2263, 2419, 2648, 2799, 3223, 3319, 3723

Offset: 0

Author

Álvar Ibeas, Sep 02 2020

Keywords

• nonn

Comments

The number of multiplicity multisets met by a positive even number of partitions of n is A088887(n) - a(n).

The parity of a(n) is A040051(n).

Examples

			The partitions of 7 exhibit 10 = A088887(7) different multisets of multiplicities. Except for (3, 1) (met by partitions (4, 1, 1, 1) and (2, 2, 2, 1)), an odd number of partitions of 7 lead to each of them, so a(7) = 9.
		

Crossrefs

Cf. A088887.

Formula

a(n) = Sum_{k odd} A337583(n, k).