cp's OEIS Frontend

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

%I A002956 M1084 #30 Nov 09 2018 14:02:34
%S A002956 1,2,4,7,15,20,48,65,119,166,348,367,827,974,1494,2135,3913,4038,7936,
%T A002956 8247,12967,17476,29162,28065,49609,59358,83420,97243,164967,152548,
%U A002956 280352,295291,405919,508162,674630,708819,1230259,1325732,1709230
%N A002956 Number of basic invariants for cyclic group of order and degree n.
%C A002956 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
%D A002956 M. D. Neusel and L. Smith, Invariant Theory of Finite Groups, Amer. Math. Soc., 2002; see p. 208.
%D A002956 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002956 C. W. Strom, Complete systems of invariants of the cyclic groups of equal order and degree, Proc. Iowa Acad. Sci., 55 (1948), 287-290.
%H A002956 Finklea, Moore, Ponomarenko and Turner, <a href="http://www-rohan.sdsu.edu/~vadim/fmpt1b-revised.pdf">Invariant Polynomials and Minimal Zero Sequences</a>, to appear in Communications in Algebra.
%H A002956 Bryson W. Finklea, Terri Moore, Vadim Ponomarenko and Zachary J. Turner, <a href="http://dx.doi.org/10.2140/involve.2008.1.159">Invariant polynomials and minimal zero sequences</a>, Involve, 1:2 (2008), pp. 159-165.
%H A002956 Vadim Ponomarenko, <a href="http://www-rohan.sdsu.edu/~vadim/Cyclic.xls">Table</a>
%H A002956 Vadim Ponomarenko, <a href="http://www-rohan.sdsu.edu/~vadim/mzs.zip">Programs</a>
%F A002956 a(n) = A096337(n) + 1. - _Filip Zaludek_, Oct 26 2016
%Y A002956 Row sums of A082641.
%Y A002956 Cf. A096337.
%K A002956 nonn,nice
%O A002956 1,2
%A A002956 _N. J. A. Sloane_
%E A002956 More terms from Vadim Ponomarenko (vadim123(AT)gmail.com), Jun 29 2004