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A109704
Number of partitions of n into parts each equal to 2 mod 7.
4
1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 3, 1, 3, 2, 3, 3, 3, 4, 3, 4, 4, 4, 6, 4, 7, 4, 8, 5, 8, 7, 8, 9, 8, 10, 9, 11, 12, 11, 15, 11, 17, 12, 18, 15, 19, 19, 19, 22, 20, 24, 24, 25, 29, 26, 34, 27, 37, 31, 39, 38, 40, 44, 42, 49, 47, 52, 55, 54, 64, 56, 71, 62, 76, 72, 79
OFFSET
0,17
LINKS
FORMULA
G.f.: 1/product(1-x^(2+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006
a(n) ~ Gamma(2/7) * exp(Pi*sqrt(2*n/21)) / (2^(23/14) * 3^(1/7) * 7^(5/14) * Pi^(5/7) * n^(9/14)) * (1 + (11*Pi/(168*sqrt(42)) - 9*sqrt(3/14)/(7*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017
a(n) = (1/n)*Sum_{k=1..n} A284443(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 28 2017
EXAMPLE
a(18)=3 because we have 18=16+2=9+9=2+2+2+2+2+2+2+2+2.
MAPLE
g:=1/product(1-x^(2+7*j), j=0..20): gser:=series(g, x=0, 87): seq(coeff(gser, x, n), n=0..84); # Emeric Deutsch, Apr 14 2006
MATHEMATICA
nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+2)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)
CROSSREFS
Sequence in context: A239930 A226859 A025820 * A073407 A049994 A135732
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