A086163 - OEIS

%I #24 Feb 12 2023 11:07:02

%S 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,

%T 65,71,77,81,90,95,100,108,116,121,132,139,145,156,167,172,185,194,

%U 202,215,228,235,250,262,273,287,302,311,329,343,356,373,390,402,424,439,454

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

%C 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.

%D G. E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Company, 1976.

%D M. Paulsen and J. Snellman, Enumerativa egenskaper hos konkava partitioner (in Swedish), Department of Mathematics, Stockholm University.

%H V. Crispin Quinonez, <a href="https://www2.math.su.se/reports/2002/7/2002-7.pdf">Integrally closed monomial ideals and powers of ideals</a>, Research Reports in Mathematics Number 7 2002, Department of Mathematics, Stockholm University.

%H Jan Snellman and Michael Paulsen, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Snellman/snellman2.html">Enumeration of Concave Integer Partitions</a>, J. Integer Seq., Vol. 7 (2004), Article 04.1.3.

%F 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)).

%t 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]

%Y Cf. A084913, A086162, A086163.

%K nonn,easy

%O 0,3

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

%E More terms from _Robert G. Wilson v_, Aug 27 2003