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

Offset: 0

Author

Andrew Weimholt, Feb 01 2011

Keywords

• nonn

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.

Examples

			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.
		

Links

• Finklea, Moore, Ponomarenko and Turner, Invariant Polynomials and Minimal Zero Sequences

Crossrefs

Cf. A000041, A002956, A082641