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A109699 Number of partitions of n into parts each equal to 3 mod 5. 3
1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 4, 2, 4, 4, 3, 5, 4, 5, 6, 5, 7, 6, 8, 8, 7, 11, 9, 10, 13, 10, 14, 14, 14, 17, 16, 19, 19, 20, 24, 21, 27, 27, 27, 33, 30, 35, 38, 36, 44, 42, 47, 51, 50, 58, 57, 63, 68, 66, 79, 76, 82, 92, 88, 101, 104, 107, 120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,17

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: 1/product(1-x^(3+5j), j=0..infinity). - Emeric Deutsch, Mar 30 2006

a(n) ~ Gamma(3/5) * exp(Pi*sqrt(2*n/15)) / (2^(9/5) * 3^(3/10) * 5^(1/5) * Pi^(2/5) * n^(4/5)) * (1 + (11*Pi/(120*sqrt(30)) - 6*sqrt(6/5)/(5*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284281(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 24 2017

EXAMPLE

a(21)=3 since 21 = 18+3 = 13+8 = 3+3+3+3+3+3+3

MAPLE

g:=1/product(1-x^(3+5*j), j=0..25): gser:=series(g, x=0, 85): seq(coeff(gser, x, n), n=0..80); # Emeric Deutsch, Mar 30 2006

MATHEMATICA

nmax=100; CoefficientList[Series[Product[1/(1-x^(5*k+3)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)

PROG

(PARI) Vec(prod(k=0, 100, 1/(1 - x^(5*k + 3))) + O(x^111)) \\ Indranil Ghosh, Mar 24 2017

CROSSREFS

Cf. A284281.

Sequence in context: A097368 A271900 A194083 * A301563 A029283 A264404

Adjacent sequences:  A109696 A109697 A109698 * A109700 A109701 A109702

KEYWORD

nonn

AUTHOR

Erich Friedman, Aug 07 2005

EXTENSIONS

More terms from Emeric Deutsch, Mar 30 2006

STATUS

approved

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Last modified May 26 13:05 EDT 2019. Contains 323586 sequences. (Running on oeis4.)