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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 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

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Last modified June 24 06:17 EDT 2021. Contains 345416 sequences. (Running on oeis4.)