A096778 Number of partitions of n with at most two even parts.

1, 1, 2, 3, 5, 7, 10, 14, 19, 26, 34, 45, 58, 75, 95, 121, 151, 189, 234, 289, 354, 433, 526, 637, 768, 923, 1105, 1319, 1569, 1861, 2202, 2597, 3056, 3587, 4201, 4908, 5723, 6658, 7732, 8961, 10367, 11971, 13802, 15884, 18253, 20942, 23992, 27445, 31353

Offset

0,3

Comments

Also number of partitions of n+4 with exactly two even parts. Example: a(3)=3 because the partitions of 7 with exactly two even parts are [4,2,1], [3,2,2] and [2,2,1,1,1]. a(n)=A116482(n+4,2). - Emeric Deutsch, Feb 21 2006

References

Fulman, Jason. Random matrix theory over finite fields. Bull. Amer. Math. Soc. (N.S.) 39 (2002), no. 1, 51--85. MR1864086 (2002i:60012). See top of page 70, Eq. 2, with k=2. - N. J. A. Sloane, Aug 31 2014

Links

Table of n, a(n) for n=0..48.

Formula

G.f.: (1/((1-x^2)*(1-x^4)))/Product(1-x^(2*i+1), i=0..infinity). More generally, g.f. for number of partitions of n with at most k even parts is (1/Product(1-x^(2*i), i=1..k))/Product(1-x^(2*i+1), i=0..infinity).

a(n) ~ 3^(3/4) * n^(1/4) * exp(Pi*sqrt(n/3)) / (8*Pi^2). - Vaclav Kotesovec, May 29 2018

Example

a(3)=3 because we have [3],[2,1] and [1,1,1].

Mathematica

CoefficientList[ Series[(1/((1 - x^2)*(1 - x^4)))/Product[1 - x^(2i + 1), {i, 0, 50}], {x, 0, 48}], x] (* Robert G. Wilson v, Aug 16 2004 *)

Crossrefs

Cf. A038348.

Cf. A116482.

Sequence in context: A238658 A116480 A023026 * A325862 A280277 A102108

Adjacent sequences: A096775 A096776 A096777 * A096779 A096780 A096781

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 16 2004

Extensions

More terms from Robert G. Wilson v, Aug 17 2004

More terms from Emeric Deutsch, Feb 21 2006

Status

approved