OFFSET

1,3

COMMENTS

Let a(n) be the number of odd partitions in the multiset intersections of the set of partitions of n with itself three times.

Form the p(n) x p(n) x p(n) matrix M of partitions of numbers ranging from 1 to n by taking the multiset intersections of all the triples of partitions of n. Then, ignoring the empty set, the number of odd partitions in M equals the number of distinct partitions in M. (Proved in Wilf et al., "A pentagonal number sieve".)

LINKS

George Beck, triple intersections of partitions.nb

Sylvie Corteel, Carla D. Savage, Herbert S. Wilf, Doron Zeilberger, A pentagonal number sieve, J. Combin. Theory Ser. A 82 (1998), no. 2, 186-192.

Eric Weisstein's World of Mathematics, Pentagonal Number Theorem

Wikipedia, Pentagonal number theorem

EXAMPLE

For an example for double intersections, see A274521.

CROSSREFS

KEYWORD

nonn,more

AUTHOR

George Beck, Jul 04 2016

STATUS

approved