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A339088
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Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 6.
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3
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1, 1, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 4, 6, 0, 0, 0, 1, 4, 6, 0, 0, 0, 1, 6, 12, 0, 0, 0, 1, 6, 18, 24, 0, 0, 1, 8, 24, 24, 0, 0, 1, 8, 30, 48, 0, 0, 1, 10, 42, 72, 0, 0, 1, 10, 48, 120, 120, 0, 1, 12, 60, 144, 120, 0, 1, 12, 72, 216, 240, 0, 1, 14, 84, 264, 360
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OFFSET
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0,9
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LINKS
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Table of n, a(n) for n=0..83.
Index entries for sequences related to compositions
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FORMULA
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G.f.: Sum_{k>=0} k! * x^(k*(3*k - 2)) / Product_{j=1..k} (1 - x^(6*j)).
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EXAMPLE
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a(21) = 6 because we have [13, 7, 1], [13, 1, 7], [7, 13, 1], [7, 1, 13], [1, 13, 7] and [1, 7, 13].
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MATHEMATICA
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nmax = 83; CoefficientList[Series[Sum[k! x^(k (3 k - 2))/Product[1 - x^(6 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
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CROSSREFS
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Cf. A005708, A016921, A032020, A032021, A109701, A280456, A337547, A337548, A339059, A339060, A339086, A339087, A339089.
Sequence in context: A227009 A144629 A271719 * A025907 A024157 A331919
Adjacent sequences: A339085 A339086 A339087 * A339089 A339090 A339091
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Nov 23 2020
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STATUS
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approved
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