A273226 G.f. is the cube of the g.f. of A006950.

1, 3, 6, 13, 27, 51, 91, 159, 273, 455, 738, 1179, 1860, 2886, 4410, 6667, 9981, 14781, 21671, 31512, 45474, 65113, 92547, 130689, 183439, 255930, 355017, 489895, 672672, 919152, 1250107, 1692846, 2282895, 3066180, 4102224, 5468160, 7263217, 9614436, 12684633, 16682276

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..10000

M. D. Hirschhorn and J. A. Sellers, Arithmetic properties of partitions with odd parts distinct, Ramanujan J. 22 (2010), 273--284.

L. Wang, Arithmetic properties of partition triples with odd parts distinct, Int. J. Number Theory, 11 (2015), 1791--1805.

L. Wang, Arithmetic properties of partition quadruples with odd parts distinct, Bull. Aust. Math. Soc., doi:10.1017/S0004972715000647.

L. Wang, New congruences for partitions where the odd parts are distinct, J. Integer Seq. (2015), article 15.4.2.

Formula

G.f.: Product_{k>=1} (1 + x^k)^3 / (1 - x^(4*k))^3, corrected by Vaclav Kotesovec, Mar 25 2017.

a(n) ~ 3*exp(sqrt(3*n/2)*Pi) / (16*n^(3/2)). - Vaclav Kotesovec, Mar 25 2017

Maple

N:= 50:
G:= mul((1+x^k)^3, k=1..N)/mul((1-x^(4*k))^3, k=1..N/4):
S:= series(G, x, N+1):
seq(coeff(S, x, j), j=0..N); # Robert Israel, Jan 21 2019

Mathematica

s = QPochhammer[-1, x]^3/(8*QPochhammer[x^4, x^4]^3) + O[x]^40; CoefficientList[s, x] (* Jean-François Alcover, May 20 2016 *)

Crossrefs

Cf. A006950.

Sequence in context: A215989 A215980 A215979 * A291726 A280563 A281283

Adjacent sequences: A273223 A273224 A273225 * A273227 A273228 A273229

Keyword

nonn

Author

M.S. Mahadeva Naika, May 18 2016

Extensions

Edited by N. J. A. Sloane, May 26 2016

Status

approved