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A109703 Number of partitions of n into parts each equal to 1 mod 7. 8
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 5, 6, 7, 7, 7, 7, 7, 8, 10, 11, 12, 12, 12, 12, 13, 15, 17, 18, 19, 19, 19, 20, 23, 26, 28, 29, 30, 30, 31, 34, 38, 41, 43, 44, 45, 46, 50, 55, 60, 63, 65, 66, 68, 72, 79, 85, 90, 93, 95, 97, 103, 111, 120, 127, 132, 135 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

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

Vaclav Kotesovec, Graph - The asymptotic ratio

FORMULA

G.f.: 1/product(1-x^(1+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006

a(n) ~ Gamma(1/7) * exp(Pi*sqrt(2*n/21)) / (2^(11/7) * 3^(1/14) * 7^(3/7) * Pi^(6/7) * n^(4/7)) * (1 - (2*sqrt(6/7)/(7*Pi) + 13*Pi/(168*sqrt(42))) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017

a(n) = (1/n)*Sum_{k=1..n} A284099(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 20 2017

EXAMPLE

a(15)=3 because we have 15=8+1+1+1+1+1+1+1=1+1+1+1+1+1+1+1+1+1+1+1+1+1+1.

MAPLE

g:=1/product(1-x^(1+7*j), j=0..20): gser:=series(g, x=0, 80): seq(coeff(gser, x, n), n=0..77); # Emeric Deutsch, Apr 14 2006

MATHEMATICA

nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+1)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)

CROSSREFS

Cf. A284099.

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), A109701 (m=6), this sequence (m=7), A277090 (m=8).

Sequence in context: A029393 A275150 A173021 * A103375 A285758 A246869

Adjacent sequences:  A109700 A109701 A109702 * A109704 A109705 A109706

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 22 19:36 EST 2018. Contains 299469 sequences. (Running on oeis4.)