login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261037 The number of overpartitions of n with restricted odd differences and smallest part both odd and overlined. 0
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 (list; graph; refs; listen; history; text; internal format)
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))).

CROSSREFS

Cf. A141094, A260890, A261035.

Sequence in context: A134591 A058611 A098613 * A280423 A143607 A193826

Adjacent sequences:  A261034 A261035 A261036 * A261038 A261039 A261040

KEYWORD

nonn

AUTHOR

Jeremy Lovejoy, Aug 07 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 5 21:18 EDT 2020. Contains 336213 sequences. (Running on oeis4.)