A304871 Triangle read by rows: T(n, k) gives the number of partitions (d1,d2,...,dm) of n such that k = d1/1 <= d2/2 <= ... <= dm/m for 1 <= k <= n.
1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 3, 1, 1, 0, 0, 0, 0, 0, 1, 4, 1, 1, 0, 0, 0, 0, 0, 0, 1, 5, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 6, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1
Offset: 1
Examples
The partitions (d1,d2,...,dm) of 9 such that 1 = d1/1 <= d2/2 <= ... <= dm/m are (1, 8), (1, 2, 6) and (1, 3, 5). So T(9, 1) = 3. First few rows are: 1; 0, 1; 1, 0, 1; 1, 0, 0, 1; 1, 0, 0, 0, 1; 2, 1, 0, 0, 0, 1; 2, 1, 0, 0, 0, 0, 1; 2, 1, 0, 0, 0, 0, 0, 1; 3, 1, 1, 0, 0, 0, 0, 0, 1; 4, 1, 1, 0, 0, 0, 0, 0, 0, 1;
Links
- Seiichi Manyama, Rows n = 1..100, flattened