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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A103260 Number of partitions of 2n prime to 3 with all odd parts occurring with multiplicity 2. The even parts occur with multiplicity 1. 2
 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 Convolution of A098884 and A003105. [corrected by Vaclav Kotesovec, Feb 07 2021] LINKS Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004. Eric Weisstein's World of Mathematics, Ramanujan Theta Functions 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 G.f.: f(x,x^5)/f(-x,-x^5) = ( Sum_{n = -oo..oo} x^(n*(3*n-2)) )/( Sum_{n = -oo..oo} (-1)^n*x^(n*(3*n-2)) ), where f(a,b) = Sum_{n = -oo..oo} a^(n*(n+1)/2)*b^(n*(n-1)/2) is Ramanujan's 2-variable theta function. Cf. A080054 and A098151. - Peter Bala, Feb 05 2021 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); # alternative program: with(gfun): series( add(x^(n*(3*n-2)), n = -6..6)/add((-1)^n*x^(n*(3*n-2)), n = -6..6), x, 100): seriestolist(%); # Peter Bala, Feb 05 2021 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, A080054, A001082, A098151. Sequence in context: A097198 A126663 A032600 * A060824 A334125 A244459 Adjacent sequences:  A103257 A103258 A103259 * A103261 A103262 A103263 KEYWORD nonn,easy AUTHOR Noureddine Chair, Feb 15 2005 EXTENSIONS Example corrected by Vaclav Kotesovec, Sep 01 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.

Last modified June 19 22:51 EDT 2021. Contains 345152 sequences. (Running on oeis4.)