A181887 - OEIS

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A181887

a(0) = 0, and for n > 0, a(n) = A002956(n) - A000041(n)

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}