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A339088 Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 6. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..83.

Index entries for sequences related to compositions

FORMULA

G.f.: Sum_{k>=0} k! * x^(k*(3*k - 2)) / Product_{j=1..k} (1 - x^(6*j)).

EXAMPLE

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].

MATHEMATICA

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]

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 23 2020

STATUS

approved

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Last modified May 24 04:32 EDT 2022. Contains 354005 sequences. (Running on oeis4.)