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A337547
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Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 3.
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7
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1, 1, 0, 0, 1, 2, 0, 1, 2, 0, 1, 4, 6, 1, 4, 6, 1, 6, 12, 1, 6, 18, 25, 8, 24, 25, 8, 30, 49, 10, 42, 73, 10, 48, 121, 132, 60, 145, 132, 72, 217, 254, 84, 265, 374, 96, 361, 616, 114, 433, 856, 846, 553, 1218, 864, 649, 1578, 1602, 817, 2180, 2340, 937, 2780, 3798, 1129, 3622
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OFFSET
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0,6
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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(12) = 6 because we have [7, 4, 1], [7, 1, 4], [4, 7, 1], [4, 1, 7], [1, 7, 4] and [1, 4, 7].
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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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