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A337548
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Number of compositions (ordered partitions) of n into distinct parts congruent to 2 mod 3.
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7
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1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 2, 1, 0, 4, 1, 6, 4, 1, 6, 6, 1, 12, 6, 1, 18, 8, 25, 24, 8, 25, 30, 10, 49, 42, 10, 73, 48, 12, 121, 60, 132, 145, 72, 134, 217, 84, 254, 265, 96, 376, 361, 114, 616, 433, 126, 858, 553, 864, 1218, 649, 882, 1580, 817, 1620, 2180, 937
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OFFSET
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0,8
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LINKS
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FORMULA
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G.f.: Sum_{k>=0} k! * x^(k*(3*k + 1)/2) / Product_{j=1..k} (1 - x^(3*j)).
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EXAMPLE
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a(15) = 6 because we have [8, 5, 2], [8, 2, 5], [5, 8, 2], [5, 2, 8], [2, 8, 5] and [2, 5, 8].
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MATHEMATICA
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nmax = 65; CoefficientList[Series[Sum[k! x^(k (3 k + 1)/2)/Product[1 - x^(3 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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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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