A121081 Number of partitions of n into parts with at most one 1 and at most one 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

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