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

1,10

Links

Seiichi Manyama, Rows n = 1..100, flattened

Example

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;

Crossrefs

Row sums give A053282.

Cf. A304871.

Sequence in context: A082647 A367627 A214018 * A161071 A161110 A161045

Adjacent sequences: A304866 A304867 A304868 * A304870 A304871 A304872

Keyword

nonn,tabf

Author

Seiichi Manyama, May 20 2018

Status

approved