A304869 Triangle read by rows: T(n, k) gives the number of partitions (d1,d2,...,dk) of n such that 0 < d1/1 <= d2/2 <= ... <= dk/k for 1 <= k <= A003056(n).
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 3, 2, 1, 1, 3, 3, 1, 1, 4, 4, 1, 1, 4, 4, 2, 1, 4, 5, 2, 1, 5, 6, 3, 1, 1, 5, 7, 4, 1, 1, 5, 8, 5, 1, 1, 6, 9, 6, 2, 1, 6, 10, 7, 2, 1, 6, 11, 9, 3, 1, 7, 13, 10, 4, 1, 1, 7, 14, 12, 5, 1, 1, 7, 15, 14, 6, 1
Offset: 1
Examples
The partitions (d1,d2) of 9 such that 0 < d1/1 <= d2/2 are (1, 8), (2, 7) and (3, 6). So T(9, 2) = 3. First few rows are: 1; 1; 1, 1; 1, 1; 1, 1; 1, 2, 1; 1, 2, 1; 1, 2, 1; 1, 3, 2; 1, 3, 2, 1; 1, 3, 3, 1; 1, 4, 4, 1; 1, 4, 4, 2; 1, 4, 5, 2; 1, 5, 6, 3, 1;
Links
- Seiichi Manyama, Rows n = 1..100, flattened