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A109698
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Number of partitions of n into parts each equal to 2 mod 5.
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3
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1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 3, 2, 3, 3, 3, 4, 4, 4, 6, 4, 7, 5, 8, 7, 8, 9, 9, 10, 12, 11, 15, 12, 17, 15, 18, 19, 20, 22, 24, 24, 29, 26, 34, 31, 37, 38, 40, 44, 46, 49, 55, 53, 64, 60, 71, 71, 77, 83, 86, 93, 100, 101, 116, 112, 130, 129, 142, 149, 156, 168, 177
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OFFSET
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0,13
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
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FORMULA
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G.f.: 1/product(1-x^(2+5j), j=0..infinity). - Emeric Deutsch, Feb 15 2006
a(n) ~ Gamma(2/5) * exp(Pi*sqrt(2*n/15)) / (2^(17/10) * 3^(1/5) * 5^(3/10)*Pi^(3/5) * n^(7/10)) * (1 + (11*Pi/(120*sqrt(30)) - 7*sqrt(3/10)/(5*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017
a(n) = (1/n)*Sum_{k=1..n} A284280(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 24 2017
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EXAMPLE
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a(12)=2 since 12 = 12 = 2+2+2+2+2+2
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MAPLE
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g:=1/product(1-x^(2+5*i), i=0..20): gser:=series(g, x=0, 86): seq(coeff(gser, x, n), n=0..82); # Emeric Deutsch, Feb 15 2006
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MATHEMATICA
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nmax=100; CoefficientList[Series[Product[1/(1-x^(5*k+2)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *)
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PROG
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(PARI) Vec(prod(k=0, 100, 1/(1 - x^(5*k + 2))) + O(x^111)) \\ Indranil Ghosh, Mar 24 2017
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CROSSREFS
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Cf. A284280.
Sequence in context: A046051 A025812 A263001 * A029231 A025808 A144079
Adjacent sequences: A109695 A109696 A109697 * A109699 A109700 A109701
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KEYWORD
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hard,nonn
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AUTHOR
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Erich Friedman, Aug 07 2005
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EXTENSIONS
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More terms from Emeric Deutsch, Feb 15 2006
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STATUS
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approved
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