A261037 The number of overpartitions of n with restricted odd differences and smallest part both odd and overlined.

1, 1, 3, 4, 7, 10, 17, 23, 36, 48, 73, 96, 140, 182, 259, 334, 463, 592, 806, 1024, 1370, 1728, 2281, 2860, 3727, 4646, 5991, 7430, 9487, 11706, 14822, 18205, 22870, 27966, 34890, 42492, 52670, 63896, 78743, 95178, 116659, 140516, 171380, 205750

Offset

1,3

Comments

The number of overpartitions of n such that: (i) the difference between successive parts may be odd only if the larger part is overlined and (ii) the smallest part of the overpartition is both odd and overlined.

Links

Table of n, a(n) for n=1..44.

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.: 1 + 3*Sum_{n >= 1} a(n)*q^n = (Product_{n >= 1} (1-q^(3*n))/((1-q^n)*(1-q^(2*n)))) * (1 + 2*Sum_{n >= 1} q^(n*(n+1)/2)*(1-q^2)*(1-q^4)*...*(1-q^(2*n-2))*(1-q^n)/((1-q^3)*(1-q^6)*...*(1-q^(3*n)))) = A260890(q)*A260983(q).

Crossrefs

Cf. A141094, A260890, A260983, A261035.

Sequence in context: A058611 A357459 A098613 * A280423 A143607 A193826

Adjacent sequences: A261034 A261035 A261036 * A261038 A261039 A261040

Keyword

nonn

Author

Jeremy Lovejoy, Aug 07 2015

Status

approved