A035964 Number of partitions in parts not of the form 17k, 17k+3 or 17k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 7 are greater than 1.

1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 78, 98, 128, 159, 204, 252, 319, 392, 490, 599, 742, 902, 1107, 1339, 1632, 1964, 2378, 2849, 3429, 4091, 4897, 5819, 6933, 8207, 9733, 11481, 13562, 15943, 18761, 21985, 25780, 30121, 35204, 41013

Offset

1,2

Comments

Case k=8,i=3 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Table of n, a(n) for n=1..47.

Formula

a(n) ~ exp(2*Pi*sqrt(7*n/51)) * 7^(1/4) * sin(3*Pi/17) / (3^(1/4) * 17^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(17*k))*(1 - x^(17*k+ 3-17))*(1 - x^(17*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A326526 A035951 A035957 * A035972 A035981 A035991

Adjacent sequences: A035961 A035962 A035963 * A035965 A035966 A035967

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved