login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027342 Number of partitions of n that do not contain 8 as a part. 2
1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 72, 94, 124, 161, 209, 267, 343, 434, 550, 691, 867, 1079, 1344, 1661, 2051, 2520, 3091, 3773, 4602, 5587, 6774, 8185, 9874, 11873, 14259, 17072, 20411, 24343, 28989, 34440, 40864, 48378, 57198, 67497, 79543 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..46.

FORMULA

G.f.: (1-x^8) Product_{m>0} 1/(1-x^m).

a(n)=A000041(n)-A000041(n-8).

a(n) ~ 2*Pi * exp(sqrt(2*n/3)*Pi) / (3*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 8*Pi/(2*sqrt(6)))/sqrt(n) + (97/8 + 9/(2*Pi^2) + 12481*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016

MATHEMATICA

Table[Count[IntegerPartitions[n], _?(FreeQ[#, 8]&)], {n, 0, 50}] (* Harvey P. Dale, Mar 11 2017 *)

PROG

(PARI) a(n)=if(n<0, 0, polcoeff((1-x^8)/eta(x+x*O(x^n)), n))

CROSSREFS

Column 8 of A175788.

Sequence in context: A035996 A261775 A036007 * A184643 A307547 A182804

Adjacent sequences:  A027339 A027340 A027341 * A027343 A027344 A027345

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Benoit Cloitre, Dec 10 2002

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 November 12 22:16 EST 2019. Contains 329079 sequences. (Running on oeis4.)