A002956 Number of basic invariants for cyclic group of order and degree n.

1, 2, 4, 7, 15, 20, 48, 65, 119, 166, 348, 367, 827, 974, 1494, 2135, 3913, 4038, 7936, 8247, 12967, 17476, 29162, 28065, 49609, 59358, 83420, 97243, 164967, 152548, 280352, 295291, 405919, 508162, 674630, 708819, 1230259, 1325732, 1709230

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

a(n) is also the number of multisets of integers ranging from 1 to n, such that the sum of the members of the multiset is congruent to 0 mod n, and no submultiset exists whose sum of members is congruent to 0 mod n. These multisets can be thought of as partitions of n in modular arithmetic, thus this sequence can be thought of as a modular arithmetic version of the partition numbers (cf. A000041). - Andrew Weimholt, Jan 31 2011

References

• M. D. Neusel and L. Smith, Invariant Theory of Finite Groups, Amer. Math. Soc., 2002; see p. 208.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• C. W. Strom, Complete systems of invariants of the cyclic groups of equal order and degree, Proc. Iowa Acad. Sci., 55 (1948), 287-290.

Links

• Finklea, Moore, Ponomarenko and Turner, Invariant Polynomials and Minimal Zero Sequences, to appear in Communications in Algebra.
• Bryson W. Finklea, Terri Moore, Vadim Ponomarenko and Zachary J. Turner, Invariant polynomials and minimal zero sequences, Involve, 1:2 (2008), pp. 159-165.
• Vadim Ponomarenko, Table
• Vadim Ponomarenko, Programs

Crossrefs

Row sums of A082641.

Cf. A096337.

Formula

a(n) = A096337(n) + 1. - Filip Zaludek, Oct 26 2016

Extensions

More terms from Vadim Ponomarenko (vadim123(AT)gmail.com), Jun 29 2004