login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A035991 Number of partitions in parts not of the form 23k, 23k+3 or 23k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 10 are greater than 1. 0
1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 79, 99, 130, 162, 209, 259, 329, 406, 510, 625, 778, 949, 1170, 1420, 1738, 2100, 2553, 3070, 3710, 4443, 5340, 6369, 7618, 9052, 10777, 12760, 15130, 17853, 21088, 24803, 29193, 34233, 40158, 46954 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=11,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(10*n/69)) * 10^(1/4) * sin(3*Pi/23) / (3^(1/4) * 23^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(23*k))*(1 - x^(23*k+ 3-23))*(1 - x^(23*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A035964 A035972 A035981 * A036002 A104504 A027337

Adjacent sequences:  A035988 A035989 A035990 * A035992 A035993 A035994

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 7 14:43 EDT 2020. Contains 336276 sequences. (Running on oeis4.)