A086163 Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^4.

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

Offset

0,3

Comments

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 not lie in the Ferrers diagram of the partition, is integrally closed.

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.

Links

Table of n, a(n) for n=0..61.

V. Crispin Quinonez, Integrally closed monomial ideals and powers of ideals, Research Reports in Mathematics Number 7 2002, Department of Mathematics, Stockholm University.

Jan Snellman and Michael Paulsen, Enumeration of Concave Integer Partitions, J. Integer Seq., Vol. 7 (2004), Article 04.1.3.

Formula

G.f.: (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)).

Mathematica

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]

Crossrefs

Cf. A084913, A086162, A086163.

Sequence in context: A071652 A089884 A172312 * A175059 A372429 A366429

Adjacent sequences: A086160 A086161 A086162 * A086164 A086165 A086166

Keyword

nonn,easy

Author

Jan Snellman (Jan.Snellman(AT)math.su.se), Aug 25 2003

Extensions

More terms from Robert G. Wilson v, Aug 27 2003

Status

approved