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A303552
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Number of periodic multisets of compositions of total weight n.
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3
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0, 1, 1, 3, 1, 9, 1, 18, 7, 44, 1, 119, 1, 246, 48, 585, 1, 1470, 1, 3248, 250, 7535, 1, 18114, 42, 40593, 1373, 93726, 1, 218665, 1, 493735, 7539, 1127981, 285, 2587962, 1, 5841445, 40597, 13244166, 1, 30047413, 1, 67604050, 216745, 152258273, 1, 342747130
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OFFSET
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1,4
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COMMENTS
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A multiset is periodic if its multiplicities have a common divisor greater than 1.
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LINKS
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EXAMPLE
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The a(6) = 9 periodic multisets of compositions are:
{1,1,1,1,1,1},
{1,1,2,2}, {1,1,11,11},
{2,2,2}, {11,11,11},
{3,3}, {21,21}, {12,12}, {111,111}.
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MATHEMATICA
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nn=60;
ser=Product[1/(1-x^n)^2^(n-1), {n, nn}]
Table[SeriesCoefficient[ser, {x, 0, n}]-Sum[MoebiusMu[d]*SeriesCoefficient[ser, {x, 0, n/d}], {d, Divisors[n]}], {n, 1, nn}]
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CROSSREFS
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Cf. A000740, A000837, A007716, A007916, A034691, A100953, A255906, A269134, A301700, A303386, A303431, A303547, A303551.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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