

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, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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), 147149.


FORMULA

G.f.: Product_{n>0} ((1q^(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 * A147753 A333355 A116531
Adjacent sequences: A336761 A336762 A336763 * A336767 A336768 A336769


KEYWORD

sign


AUTHOR

Jeremy Lovejoy, Aug 04 2020


STATUS

approved



