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

Author

Reinhard Zumkeller, Aug 11 2006

Keywords

• nonn

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]

Examples

			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.

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