A335755 a(n) is the number of overpartitions of n where overlined parts are not divisible by 3 and non-overlined parts are congruent to 2 modulo 3.

1, 1, 2, 2, 3, 5, 6, 9, 11, 14, 19, 24, 31, 39, 48, 61, 75, 93, 114, 139, 169, 205, 248, 298, 358, 428, 510, 607, 719, 851, 1005, 1182, 1389, 1628, 1904, 2225, 2592, 3015, 3501, 4058, 4698, 5429, 6264, 7216, 8302, 9538, 10944, 12541, 14351, 16403

Offset

0,3

Links

Table of n, a(n) for n=0..49.

J. Lovejoy, Asymmetric generalizations of Schur's theorem, in: Andrews G., Garvan F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham.

Formula

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

a(n) ~ Pi^(2/3) * exp(2*Pi*sqrt(n)/3) / (3*sqrt(2)*Gamma(1/3)*n^(5/6)). - Vaclav Kotesovec, Jan 14 2021

Example

The 6 overpartitions counted by a(6) are: [5,1'], [5',1'], [4',2], [4',2'], [2,2,2], [2',2,2].

Mathematica

nmax = 60; CoefficientList[Series[Product[(1 + x^(3*k-1)) * (1 + x^(3*k-2)) / (1 - x^(3*k-1)), {k, 1, nmax/3}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 14 2021 *)

Crossrefs

Cf. A003105, A015128, A098151, A335754.

Sequence in context: A326687 A352524 A172993 * A325338 A143438 A004037

Adjacent sequences: A335752 A335753 A335754 * A335756 A335757 A335758

Keyword

nonn

Author

Jeremy Lovejoy, Jun 20 2020

Status

approved