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A301563
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Expansion of Product_{k>=0} (1 + x^(5*k+1))*(1 + x^(5*k+3)).
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7
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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
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OFFSET
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0,10
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COMMENTS
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Number of partitions of n into distinct parts congruent to 1 or 3 mod 5.
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LINKS
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Table of n, a(n) for n=0..72.
Index entries for sequences related to partitions
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FORMULA
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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
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EXAMPLE
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a(14) = 3 because we have [13, 1], [11, 3] and [8, 6].
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MATHEMATICA
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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]
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CROSSREFS
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Cf. A035372, A047219, A107234, A107236, A203776, A219607, A280454, A281271, A301562, A301564, A301565, A301567, A301568, A301569, A301570.
Sequence in context: A271900 A194083 A109699 * A330896 A328294 A029283
Adjacent sequences: A301560 A301561 A301562 * A301564 A301565 A301566
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Mar 23 2018
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STATUS
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approved
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