A337547 Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 3.

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

Offset

0,6

Links

Table of n, a(n) for n=0..65.

Index entries for sequences related to compositions

Formula

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

Example

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].

Mathematica

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]

Crossrefs

Cf. A000930, A016777, A032020, A032021, A035382, A261612, A337548, A339059, A339060.

Sequence in context: A351637 A029300 A096397 * A291969 A321434 A103919

Adjacent sequences: A337544 A337545 A337546 * A337548 A337549 A337550

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 22 2020

Status

approved