



0, 0, 0, 1, 2, 8, 9, 33, 43, 89, 124, 292, 290, 726, 839, 1318, 1904, 3616, 3653, 7446, 7620, 12175, 16474, 27907, 26490, 47651, 56922, 80410, 93525, 160402, 146944, 273510, 286942, 395776, 495852, 659747, 690842
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OFFSET

0,5


COMMENTS

A002956 can be thought of as a modular arithmetic version of the partition numbers (A000041). The number of "modulo n" partitions of n is the number of multisets of integers ranging from 1 to n, such that the sum of members of the multiset is congruent to 0 mod n, and no submultiset exists whose members sum to 0 mod n. Therefore, a(n) is the number of "modulo n" partitions which are not ordinary partitions of n.


LINKS

Table of n, a(n) for n=0..36.
Finklea, Moore, Ponomarenko and Turner, Invariant Polynomials and Minimal Zero Sequences


EXAMPLE

The multisets counted by A002956(5) but not by A000041(5) are
..{1,3,3,3}
..{2,2,2,2,2}
..{2,2,2,4}
..{2,4,4}
..{3,3,3,3,3}
..{3,4,4,4}
..{3,3,4}
..{4,4,4,4,4}
So a(5) = 8.


CROSSREFS

Cf. A000041, A002956, A082641
Sequence in context: A075644 A088825 A337706 * A221049 A181476 A055678
Adjacent sequences: A181884 A181885 A181886 * A181888 A181889 A181890


KEYWORD

nonn


AUTHOR

Andrew Weimholt, Feb 01 2011


STATUS

approved



