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A086161
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Number of monomial ideals in two variables x, y that are artinian, integrally closed, of colength n and contain x^2.
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2
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1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Alternatively, "concave partitions" of n with at most 2 parts, where a concave partition is defined by demanding that the monomial ideal, generated by the monomials whose exponents do no lie in the Ferrers diagram of the partition, is integrally closed.
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REFERENCES
| G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Company, 1976.
M. Paulsen and J. Snellman, Enumerativa egenskaper hos konkava partitioner (in Swedish), Department of Mathematics, Stockholm University.
V. Crispin Quinonez, Integrally closed monomial ideals and powers of ideals, Research Reports in Mathematics Number 7 2002, Department of Mathematics, Stockholm University
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LINKS
| Jan Snellman and Michael Paulsen, Enumeration of Concave Integer Partitions, J. Integer Seqs., Vol. 7, 2004.
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FORMULA
| generating function = (1+x^2-x^3)/((1-x)*(1-x^3))
a(n)=A008620(n+1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 12 2008]
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CROSSREFS
| Cf. A084913.
Cf. A084913, A086162, A086163.
Sequence in context: A172264 A079001 A032615 * A002264 A008620 A104581
Adjacent sequences: A086158 A086159 A086160 * A086162 A086163 A086164
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KEYWORD
| nonn
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AUTHOR
| Jan Snellman (Jan.Snellman(AT)math.su.se), Aug 25 2003
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