A261035 A weighted count of the number of overpartitions of n with restricted odd differences.

1, -1, -1, -1, 2, -1, 4, -5, 7, -8, 10, -15, 18, -22, 26, -37, 46, -53, 66, -84, 104, -122, 148, -183, 224, -263, 312, -379, 454, -531, 626, -750, 887, -1034, 1208, -1428, 1672, -1936, 2250, -2633, 3062, -3529, 4076, -4728, 5460, -6264, 7196, -8290, 9520, -10875, 12431, -14238

Offset

0,5

Comments

The number of overpartitions of n counted with weight (-1)^(the largest part) and such that: (i) the difference between successive parts may be odd only if the larger part is overlined and (ii) if the smallest part of the overpartition is odd then it is overlined.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Alois P. Heinz)

K. Bringmann, J. Dousse, J. Lovejoy, and K. Mahlburg, Overpartitions with restricted odd differences, Electron. J. Combin. 22 (2015), no.3, paper 3.17

Formula

G.f.: Product_{n >= 1} (1+q^(3*n))/(1+q^n)^3 * (1 + 2*Sum_{n >= 1} q^(n(n+1)/2)*(1+q)^2(1+q^2)^2...(1+q^(n-1))^2*(1+q^n)/((1+q^3)(1+q^6)...(1+q^(3*n))).

a(n) ~ (-1)^n * exp(2*Pi*sqrt(n)/3) / (2 * 3^(3/2) * n^(3/4)). - Vaclav Kotesovec, Jun 12 2019

Crossrefs

Cf. A260890. Equals the convolution of A141094 and A260984.

Sequence in context: A021992 A337123 A292388 * A080030 A337589 A125156

Adjacent sequences: A261032 A261033 A261034 * A261036 A261037 A261038

Keyword

sign

Author

Jeremy Lovejoy, Aug 07 2015

Status

approved