A277210 Expansion of Product_{k>=1} 1/(1 - x^(3*k+1)).

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 3, 3, 4, 5, 4, 6, 6, 7, 7, 9, 8, 11, 11, 12, 13, 16, 15, 18, 20, 22, 22, 27, 27, 31, 33, 37, 38, 45, 46, 51, 55, 62, 63, 72, 76, 84, 89, 99, 103, 116, 122, 133, 142, 158, 164, 181, 193, 210, 222, 245, 257, 281, 299, 324, 343, 376, 396, 429, 457, 495, 522, 568, 601, 649, 689

Offset

0,15

Comments

Number of partitions of n into parts larger than 1 and congruent to 1 mod 3.

More generally, the ordinary generating function for the number of partitions of n into parts larger than 1 and congruent to 1 mod m (for m>0) is Product_{k>=1} 1/(1 - x^(m*k+1)).

Links

Table of n, a(n) for n=0..85.

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} 1/(1 - x^(3*k+1)).

a(n) ~ Pi^(1/3) * Gamma(1/3) * exp(sqrt(2*n)*Pi/3) / (2^(13/6)*3^(3/2)*n^(7/6)). - Vaclav Kotesovec, Oct 06 2016

Example

a(14) = 2, because we have [10, 4] and [7, 7].

Mathematica

CoefficientList[Series[(1 - x)/QPochhammer[x, x^3], {x, 0, 85}], x]

Crossrefs

Cf. A016777, A035382, A087897, A117957.

Sequence in context: A146879 A231577 A325590 * A304777 A058762 A241314

Adjacent sequences: A277207 A277208 A277209 * A277211 A277212 A277213

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 05 2016

Status

approved