login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A121081 Number of partitions of n into parts with at most one 1 and at most one 2. 2
1, 1, 2, 2, 3, 5, 6, 8, 11, 14, 18, 24, 30, 38, 49, 61, 76, 96, 118, 146, 181, 221, 270, 331, 401, 486, 589, 709, 852, 1025, 1225, 1463, 1746, 2075, 2463, 2922, 3453, 4077, 4808, 5656, 6644, 7798, 9130, 10678, 12475, 14547, 16942, 19714, 22898, 26570, 30798 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

a(n) is also the number of partitions of n with no part equal to 2 or 4. [From Shanzhen Gao, Oct 28 2010]

LINKS

Table of n, a(n) for n=1..51.

FORMULA

a(n) = A121659(n) + A008483(n-3) for n>2. - Reinhard Zumkeller, Aug 14 2006

G.f.: (1+x)*(1+x^2)/Product_{k>=3} (1-x^k). - Vladeta Jovovic, Aug 13 2006

a(n) = A000041(n)-A000041(n-2)-A000041(n-4)+A000041(n-6), n>5. - Vladeta Jovovic, Aug 13 2006

Given by p(n)-p(n-2)-p(n-4)+p(n-6) where p(n)=A000041(n). - Shanzhen Gao, Oct 28 2010

a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^2 / (3^(3/2) * n^2). - Vaclav Kotesovec, Jun 02 2018

EXAMPLE

a(8)=#{8,7+1,6+2,5+3,5+2+1,4+4,4+3+1,3+3+2}=8;

a(9)=#{9,8+1,7+2,6+3,6+2+1,5+4,5+3+1,4+4+1,4+3+2,3+3+3,3+3+2+1}=11.

CROSSREFS

Cf. A027336.

Sequence in context: A052337 A308858 A192432 * A330952 A118399 A278298

Adjacent sequences: A121078 A121079 A121080 * A121082 A121083 A121084

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 11 2006

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 6 01:28 EST 2023. Contains 360091 sequences. (Running on oeis4.)