OFFSET
0,3
COMMENTS
The number of overpartitions of n where (i) the difference between successive parts may be odd only if the larger is overlined and (ii) if the smallest part is overlined, then it is odd.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
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)*(1-q^(2*n))).
a(n) ~ sqrt(21) * exp(Pi*sqrt(7*n)/3) / (36*n). - Vaclav Kotesovec, Jun 13 2019
MAPLE
with(numtheory):
a:= proc(n) option remember;
`if`(n=0, 1, add(add(d*[1, 1, 2, 0, 2, 1]
[irem(d, 6)+1], d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..60); # Alois P. Heinz, Aug 08 2015
MATHEMATICA
QP = QPochhammer; QP[q^3]/(QP[q] QP[q^2]) + O[q]^50 // CoefficientList[#, q]& (* Jean-François Alcover, Mar 23 2017 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Jeremy Lovejoy, Aug 06 2015
STATUS
approved