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

1,16

Links

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

Example

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;

Crossrefs

Row sums give A053282.

Cf. A304869.

Sequence in context: A064662 A352193 A024944 * A362370 A117907 A300069

Adjacent sequences: A304868 A304869 A304870 * A304872 A304873 A304874

Keyword

nonn,tabl

Author

Seiichi Manyama, May 20 2018

Status

approved