A086161 Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^2.

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, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 25

Offset

0,3

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 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..73.

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 Seqs., Vol. 7, 2004.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

G.f.: (1 + x^2 - x^3)/((1 - x)*(1 - x^3)).

a(n) = A008620(n+1). - R. J. Mathar, Sep 12 2008

E.g.f.: (3*exp(x)*(3 + x) - 2*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Feb 11 2023

Prog

(PARI) Vec((1+x^2-x^3)/((1-x)*(1-x^3)) + O(x^80)) \\ Michel Marcus, May 22 2015

Crossrefs

Cf. A008620, A084913, A086162, A086163.

Sequence in context: A261231 A296357 A002264 * A008620 A104581 A261916

Adjacent sequences: A086158 A086159 A086160 * A086162 A086163 A086164

Keyword

nonn,easy

Author

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

Status

approved