A337548 Number of compositions (ordered partitions) of n into distinct parts congruent to 2 mod 3.

1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 2, 1, 0, 4, 1, 6, 4, 1, 6, 6, 1, 12, 6, 1, 18, 8, 25, 24, 8, 25, 30, 10, 49, 42, 10, 73, 48, 12, 121, 60, 132, 145, 72, 134, 217, 84, 254, 265, 96, 376, 361, 114, 616, 433, 126, 858, 553, 864, 1218, 649, 882, 1580, 817, 1620, 2180, 937

Offset

0,8

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(15) = 6 because we have [8, 5, 2], [8, 2, 5], [5, 8, 2], [5, 2, 8], [2, 8, 5] and [2, 5, 8].

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. A000931, A016789, A032020, A032021, A035386, A262928, A337547, A339059, A339060.

Sequence in context: A357022 A025841 A138468 * A029296 A096419 A283616

Adjacent sequences: A337545 A337546 A337547 * A337549 A337550 A337551

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 22 2020

Status

approved