A336766 The number of partitions of n into an even number of parts, each part occurring at most five times, minus the number of partitions of n into an odd number of parts, each part occurring at most five times.

1, -1, 0, -1, 1, -1, 0, 0, 2, -1, 1, -1, 1, -1, 1, -1, 2, -2, 1, -2, 2, -2, 1, -2, 3, -3, 2, -2, 3, -3, 3, -3, 4, -4, 3, -4, 5, -4, 4, -4, 6, -5, 5, -6, 6, -7, 6, -6, 8, -8, 7, -8, 9, -9, 8, -9, 11, -11, 10, -11, 12, -12, 11, -13, 15, -15, 14, -15, 17, -17, 16, -17

Offset

0,9

Links

Table of n, a(n) for n=0..71.

H. L. Alder and A. A. Muwafi, Identities relating the number of partitions into an even and odd number of parts, Fibonacci Quarterly, 13 (1975), 147-149.

Formula

G.f.: Product_{n>0} ((1-q^(6*n))/(1+q^n)).

Example

There are 10 partitions of 6 where parts occur at most five times: 6, 5+1, 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, 2+2+1+1, 2+1+1+1+1, and so a(6) = 0.

Crossrefs

Cf. A000041, A106459, A219601, A336767.

Sequence in context: A107039 A249771 A030615 * A375732 A147753 A333355

Adjacent sequences: A336763 A336764 A336765 * A336767 A336768 A336769

Keyword

sign

Author

Jeremy Lovejoy, Aug 04 2020

Status

approved