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A181887 a(0) = 0, and for n > 0, a(n) = A002956(n) - A000041(n) 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A337706 A368341 A369649 * A221049 A181476 A055678
KEYWORD
nonn
AUTHOR
Andrew Weimholt, Feb 01 2011
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)