A110619 Triangle of number of partitions of n with no part more than n/k; also partitions of n into n/k or fewer parts.

1, 2, 1, 3, 1, 1, 5, 3, 1, 1, 7, 3, 1, 1, 1, 11, 7, 4, 1, 1, 1, 15, 8, 4, 1, 1, 1, 1, 22, 15, 5, 5, 1, 1, 1, 1, 30, 18, 12, 5, 1, 1, 1, 1, 1, 42, 30, 14, 6, 6, 1, 1, 1, 1, 1, 56, 37, 16, 6, 6, 1, 1, 1, 1, 1, 1, 77, 58, 34, 19, 7, 7, 1, 1, 1, 1, 1, 1, 101, 71, 39, 21, 7, 7, 1, 1, 1, 1, 1, 1, 1, 135, 105

Offset: 1

Author

Henry Bottomley, Aug 01 2005

Keywords

• nonn
• tabl

Examples

			Rows start: 1; 2,1; 3,1,1; 5,3,1,1; 7,3,1,1,1; 11,7,4,1,1,1; etc.
T(7,3)=4 since 7 can be partitioned as 1+1+1+1+1+1+1, 2+1+1+1+1+1, 2+2+1+1+1, or 2+2+2+1 and also as 7, 6+1, 5+2, or 4+3.
		

Crossrefs

First column is A000041, second is A110618.

Formula

T(n, k)=A008284(n+floor[n/k], floor[n/k]). T(0, k)=1; T(n, k)=0 for 0A000041(n); T(n, 2)=A110618(n).