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A082641
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Triangle T(n,k) (n >= 1, 1 <= k <= n) read by rows, where T(n,k) = number of basic invariants of degree k for the cyclic group of order and degree n.
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2
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1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 4, 4, 4, 1, 3, 6, 6, 2, 2, 1, 3, 8, 12, 12, 6, 6, 1, 4, 10, 18, 16, 8, 4, 4, 1, 4, 14, 26, 32, 18, 12, 6, 6, 1, 5, 16, 36, 48, 32, 12, 8, 4, 4, 1, 5, 20, 50, 82, 70, 50, 30, 20, 10, 10, 1, 6, 24, 64, 104, 84, 36, 20, 12, 8, 4, 4, 1, 6, 28, 84, 168, 180, 132, 84, 60, 36, 24, 12, 12, 1, 7, 32, 104, 216, 242, 162, 96, 42, 30, 18, 12, 6, 6
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| T(n,k) is also the number of multisets of k 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 sum of members is congruent to 0 mod n. - Andrew Weimholt, Jan 31 2011
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REFERENCES
| M. D. Neusel and L. Smith, Invariant Theory of Finite Groups, Amer. Math. Soc., 2002; see p. 208.
C. W. Strom, Complete systems of invariants of the cyclic groups of equal order and degree, Proc. Iowa Acad. Sci., 55 (1948), 287-290.
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LINKS
| Finklea, Moore, Ponomarenko and Turner, Invariant Polynomials and Minimal Zero Sequences, to appear in Communications in Algebra.
Vadim Ponomarenko, Table (Excel spread-sheet format)
Vadim Ponomarenko, Programs
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EXAMPLE
| 1; 1,1; 1,1,2; 1,2,2,2; 1,2,4,4,4; ...
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CROSSREFS
| Row sums give A002956.
Sequence in context: A043555 A118821 A118824 * A138553 A069016 A071414
Adjacent sequences: A082638 A082639 A082640 * A082642 A082643 A082644
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 15 2003
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EXTENSIONS
| More terms from Vadim Ponomarenko (vadim123(AT)gmail.com), Jun 29 2004
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