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Search: id:A086163
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| A086163 |
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Number of monomial ideals in two variables x, y that are artinian, integrally closed, of colength n, and contain x^4. |
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4
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| 1, 1, 2, 3, 4, 6, 7, 7, 10, 13, 13, 16, 18, 19, 23, 27, 28, 32, 36, 39, 43, 48, 50, 56, 61, 65, 71, 77, 81, 90, 95, 100, 108, 116, 121, 132, 139, 145, 156, 167, 172, 185, 194, 202, 215, 228, 235, 250, 262, 273, 287, 302, 311, 329, 343, 356, 373, 390, 402, 424, 439, 454
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Alternatively, "concave partitions" of n with at most 4 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
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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
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Jan Snellman and Michael Paulsen, Enumeration of Concave Integer Partitions, J. Integer Seqs., Vol. 7, 2004.
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FORMULA
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generating function = (1+t^2+t^4+t^5-t^6-t^7+2*t^9-2*t^10 -t^11 -2*t^12 + 2*t^13 -t^14 -t^15 +t^16 +t^17 +t^18-t^19)/((1-t)*(1-t^3)*(1-t^6)*(1-t^10))
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MATHEMATICA
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CoefficientList[ Series[ (1 + t^2 + t^4 + t^5 - t^6 - t^7 + 2*t^9 - 2*t^10 - t^11 - 2*t^12 + 2*t^13 - t^14 - t^15 + t^16 + t^17 + t^18 - t^19) / ((1 - t)*(1 - t^3)*(1 - t^6)*(1 - t^10)), {t, 0, 65}], t]
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CROSSREFS
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Cf. A084913.
Cf. A084913, A086162, A086163.
Adjacent sequences: A086160 A086161 A086162 this_sequence A086164 A086165 A086166
Sequence in context: A072766 A071652 A089884 this_sequence A071789 A131870 A004724
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KEYWORD
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nonn
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AUTHOR
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Jan Snellman (Jan.Snellman(AT)math.su.se), Aug 25 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 27 2003
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