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

Author

Jeremy Lovejoy, Aug 07 2015

Keywords

• nonn

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

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

Crossrefs

Cf. A141094, A260890, A260983, A261035.

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).