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A109701 Number of partitions of n into parts each equal to 1 mod 6. 9
1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 7, 7, 7, 7, 8, 10, 11, 12, 12, 12, 13, 15, 17, 18, 19, 19, 20, 23, 26, 28, 29, 30, 31, 34, 38, 41, 43, 44, 46, 50, 55, 60, 63, 65, 67, 72, 79, 85, 90, 93, 96, 102, 111, 120, 127, 132, 136, 143, 154, 166, 176, 183, 189, 198 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

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

FORMULA

G.f.: 1/product(1-x^(1+6j), j=0..infinity). - Emeric Deutsch, Apr 14 2006

a(n) ~ Gamma(1/6) * exp(Pi*sqrt(n)/3) / (4 * sqrt(3) * Pi^(5/6) * n^(7/12)) * (1 - (7/(24*Pi) + Pi/144) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284098(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 20 2017

EXAMPLE

a(10)=2 since 10 = 7+1+1+1 = 1+1+1+1+1+1+1+1+1+1

MAPLE

g:=1/product(1-x^(1+6*j), j=0..20): gser:=series(g, x=0, 77): seq(coeff(gser, x, n), n=0..74); # Emeric Deutsch, Apr 14 2006

MATHEMATICA

nmax=100; CoefficientList[Series[Product[1/(1-x^(6*k+1)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)

CROSSREFS

Cf. A284098.

Cf. similar sequences of number of partitions of n into parts congruent to 1 mod m: A000009 (m=2), A035382 (m=3), A035451 (m=4), A109697 (m=5), this sequence (m=6), A109703 (m=7), A277090 (m=8).

Sequence in context: A086394 A029226 A093354 * A124751 A103374 A208251

Adjacent sequences:  A109698 A109699 A109700 * A109702 A109703 A109704

KEYWORD

nonn

AUTHOR

Erich Friedman, Aug 07 2005

EXTENSIONS

Changed offset to 0 and added a(0)=1 by Vaclav Kotesovec, Feb 27 2015

STATUS

approved

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Last modified February 19 05:12 EST 2018. Contains 299330 sequences. (Running on oeis4.)