

A109706


Number of partitions of n into parts each equal to 4 mod 7.


4



1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 1, 4, 3, 2, 2, 5, 3, 2, 4, 6, 3, 3, 6, 6, 3, 6, 7, 6, 4, 9, 8, 6, 7, 11, 8, 7, 11, 12, 8, 11, 14, 13, 9, 16, 16, 13, 13, 21, 17, 14, 20, 24, 18, 19, 26, 26, 19, 27, 31, 27, 24, 36, 34, 29, 34, 43
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OFFSET

0,23


LINKS



FORMULA

G.f.: 1/product(1x^(4+7j), j=0..infinity).  Emeric Deutsch, Apr 14 2006
a(n) ~ Gamma(4/7) * exp(Pi*sqrt(2*n/21)) / (2^(25/14) * 3^(2/7) * 7^(3/14) * Pi^(3/7) * n^(11/14)) * (1 + (23*Pi/(168*sqrt(42))  11*sqrt(6/7)/(7*Pi)) / sqrt(n)).  Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017


EXAMPLE

a(22)=2 because we have 22=18+4=11+11.


MAPLE

g:=1/product(1x^(4+7*j), j=0..20): gser:=series(g, x=0, 93): seq(coeff(gser, x, n), n=0..90); # Emeric Deutsch, Apr 14 2006


MATHEMATICA

nmax=100; CoefficientList[Series[Product[1/(1x^(7*k+4)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



