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A301563 Expansion of Product_{k>=0} (1 + x^(5*k+1))*(1 + x^(5*k+3)). 7
1, 1, 0, 1, 1, 0, 1, 1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 4, 3, 4, 4, 4, 6, 4, 6, 7, 5, 9, 8, 8, 11, 9, 12, 12, 12, 16, 13, 17, 19, 17, 23, 21, 24, 27, 24, 32, 30, 32, 40, 35, 43, 45, 44, 53, 50, 59, 62, 61, 75, 70, 78, 87, 83, 99, 97, 105, 118, 112, 133, 134, 138, 159, 153 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

Number of partitions of n into distinct parts congruent to 1 or 3 mod 5.

LINKS

Table of n, a(n) for n=0..72.

Index entries for sequences related to partitions

FORMULA

G.f.: Product_{k>=1} (1 + x^A047219(k)).

a(n) ~ exp(Pi*sqrt(2*n/15)) / (2^(21/20) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Mar 24 2018

EXAMPLE

a(14) = 3 because we have [13, 1], [11, 3] and [8, 6].

MATHEMATICA

nmax = 72; CoefficientList[Series[Product[(1 + x^(5 k + 1)) (1 + x^(5 k + 3)), {k, 0, nmax}], {x, 0, nmax}], x]

nmax = 72; CoefficientList[Series[QPochhammer[-x, x^5] QPochhammer[-x^3, x^5], {x, 0, nmax}], x]

nmax = 72; CoefficientList[Series[Product[(1 + Boole[MemberQ[{1, 3}, Mod[k, 5]]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A035372, A047219, A107234, A107236, A203776, A219607, A280454, A281271, A301562, A301564, A301565, A301567, A301568, A301569, A301570.

Sequence in context: A271900 A194083 A109699 * A029283 A264404 A116482

Adjacent sequences:  A301560 A301561 A301562 * A301564 A301565 A301566

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 23 2018

STATUS

approved

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Last modified May 21 15:00 EDT 2019. Contains 323443 sequences. (Running on oeis4.)