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!)
A035994 Number of partitions of n into parts not of the form 23k, 23k+6 or 23k-6. Also number of partitions with at most 5 parts of size 1 and differences between parts at distance 10 are greater than 1. 0
1, 2, 3, 5, 7, 10, 14, 20, 27, 37, 49, 66, 86, 113, 146, 189, 240, 307, 387, 489, 611, 764, 947, 1175, 1446, 1779, 2176, 2660, 3233, 3928, 4749, 5737, 6902, 8295, 9934, 11884, 14170, 16877, 20045, 23780, 28136, 33254, 39210, 46180, 54273, 63711 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Case k=11,i=6 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..46.

FORMULA

a(n) ~ exp(2*Pi*sqrt(10*n/69)) * 10^(1/4) * cos(11*Pi/46) / (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+ 6-23))*(1 - x^(23*k- 6))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A219601 A035975 A035984 * A036005 A104503 A027340

Adjacent sequences:  A035991 A035992 A035993 * A035995 A035996 A035997

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 July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)