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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, 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
0,3
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).
FORMULA
a(n) = Sum_{k odd} A337583(n, k).
EXAMPLE
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.
Sequence in context: A346248 A211245 A107473 * A105574 A105562 A323704
KEYWORD
nonn
AUTHOR
Álvar Ibeas, Sep 02 2020
STATUS
approved