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A103260 Number of partitions of 2n prime to 3 with all odd parts occurring with multiplicity 2. The even parts occur with multiplicity 1. 0
1, 2, 2, 2, 2, 4, 6, 8, 10, 10, 12, 16, 22, 28, 32, 36, 42, 52, 66, 80, 92, 104, 120, 144, 174, 206, 236, 266, 304, 356, 420, 488, 554, 624, 708, 816, 946, 1084, 1224, 1372, 1548, 1764, 2016, 2288, 2568, 2868, 3216, 3632, 4110 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is also the sequence A098884/A003105.

LINKS

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

Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004.

FORMULA

G.f.: (Theta_4(0, x^2)*theta_4(0, x^3))/(theta_4(0, x)*theta_4(0, x^(6))) = Product_{k>0}((1+x^(6*k-1))*(1+x^(6*k-5)))/((1-x^(6*k-1))*(1-x^(6*k-5))).

Euler transform of period 12 sequence [2, -1, 0, 0, 2, 0, 2, 0, 0, -1, 2, 0, ...]. - Vladeta Jovovic, Feb 17 2005

a(n) ~ exp(Pi*sqrt(n/3)) / (2^(3/2) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 01 2015

EXAMPLE

E.g. a(7)=8 because 14=10+4=10+2+1+1=8+4+2=8+4+1+1=7+7=5+5+4=5+5+2+1+1.

MAPLE

series(product(((1+x^(6*k-1))*(1+x^(6*k-5)))/((1-x^(6*k-1))*(1-x^(6*k-5))), k=1..100), x=0, 100);

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[((1+x^(6*k-1))*(1+x^(6*k-5)))/((1-x^(6*k-1))*(1-x^(6*k-5))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 01 2015 *)

CROSSREFS

Cf. A003105, A098884 and A080054.

Sequence in context: A097198 A126663 A032600 * A060824 A334125 A244459

Adjacent sequences:  A103257 A103258 A103259 * A103261 A103262 A103263

KEYWORD

nonn

AUTHOR

Noureddine Chair, Feb 15 2005

EXTENSIONS

Example corrected by Vaclav Kotesovec, Sep 01 2015

STATUS

approved

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Last modified September 24 01:21 EDT 2020. Contains 337315 sequences. (Running on oeis4.)