A339089 Number of compositions (ordered partitions) of n into distinct parts congruent to 5 mod 6.

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 4, 1, 0, 0, 0, 6, 4, 1, 0, 0, 0, 6, 6, 1, 0, 0, 0, 12, 6, 1, 0, 0, 0, 18, 8, 1, 0, 0, 24, 24, 8, 1, 0, 0, 24, 30, 10, 1, 0, 0, 48, 42, 10, 1, 0, 0, 72, 48, 12, 1, 0, 0, 120, 60, 12, 1, 0, 120, 144

Offset

0,17

Links

Table of n, a(n) for n=0..86.

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(33) = 6 because we have [17, 11, 5], [17, 5, 11], [11, 17, 5], [11, 5, 17], [5, 17, 11] and [5, 11, 17].

Mathematica

nmax = 86; 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. A016969, A017837, A032020, A032021, A109702, A281244, A337547, A337548, A339059, A339060, A339086, A339087, A339088.

Sequence in context: A307710 A112207 A112208 * A048158 A275342 A246838

Adjacent sequences: A339086 A339087 A339088 * A339090 A339091 A339092

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved