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A116634 Number of partitions of n having exactly one part that is a multiple of 3. 2
0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 14, 20, 26, 36, 47, 62, 80, 104, 132, 169, 212, 267, 332, 414, 510, 629, 769, 941, 1142, 1386, 1672, 2016, 2417, 2897, 3455, 4118, 4888, 5796, 6849, 8085, 9513, 11182, 13107, 15347, 17923, 20910, 24338, 28298, 32833, 38054, 44021 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Column 1 of A116633.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: x^3/((1-x^3)*Product_{j>=1} ((1-x^(3j-2))(1-x^(3j-1))).

a(n) ~ exp(2*Pi*sqrt(n)/3) / (6*Pi*n^(1/4)). - Vaclav Kotesovec, Mar 07 2016

EXAMPLE

a(7)=5 because we have [6,1],[4,3],[3,2,2],[3,2,1,1] and [3,1,1,1,1].

MAPLE

g:=x^3/(1-x^3)/product((1-x^(3*j-2))*(1-x^(3*j-1)), j=1..30): gser:=series(g, x=0, 56): seq(coeff(gser, x, n), n=0..53);

MATHEMATICA

nmax = 50; CoefficientList[Series[x^3/(1-x^3) * Product[1/((1-x^(3*k-2))*(1-x^(3*k-1))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2016 *)

CROSSREFS

Cf. A116633, A000726.

Sequence in context: A155167 A325858 A237269 * A035960 A288254 A023893

Adjacent sequences:  A116631 A116632 A116633 * A116635 A116636 A116637

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 19 2006

STATUS

approved

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Last modified June 24 22:23 EDT 2019. Contains 324337 sequences. (Running on oeis4.)