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A109705
Number of partitions of n into parts each equal to 3 mod 7.
4
1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 1, 2, 4, 2, 2, 4, 4, 2, 4, 5, 3, 4, 6, 5, 4, 6, 7, 5, 6, 8, 8, 6, 9, 11, 7, 9, 13, 10, 9, 14, 14, 10, 15, 17, 14, 15, 19, 19, 16, 20, 24, 20, 21, 27, 27, 22, 29, 33, 27, 30, 38, 35, 32, 41, 44, 37, 43, 51, 47, 45
OFFSET
0,21
LINKS
FORMULA
G.f.: 1/product(1-x^(3+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006
a(n) ~ Gamma(3/7) * exp(Pi*sqrt(2*n/21)) / (2^(12/7) * 3^(3/14) * 7^(2/7) * Pi^(4/7) * n^(5/7)) * (1 + (23*Pi/(168*sqrt(42)) - 15*sqrt(3/14)/(7*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017
a(n) = (1/n)*Sum_{k=1..n} A284444(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 28 2017
EXAMPLE
a(20)=2 because we have 20=17+3=10+10.
MAPLE
g:=1/product(1-x^(3+7*j), j=0..20): gser:=series(g, x=0, 90): seq(coeff(gser, x, n), n=0..87); # Emeric Deutsch, Apr 14 2006
MATHEMATICA
nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+3)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)
CROSSREFS
Sequence in context: A115268 A103610 A305875 * A352578 A278341 A276520
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