A274109 Triangle read by rows: T(n,k) = number of partitions of n into exactly k parts with exactly two different sizes, the sizes being relatively prime (n >= 3, 2 <= k <= n-1).

1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 3, 2, 3, 2, 2, 1, 2, 2, 4, 1, 3, 2, 2, 1, 5, 5, 3, 4, 2, 3, 2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 1, 6, 6, 4, 5, 2, 4, 2, 3, 2, 2, 1, 3, 3, 5, 3, 4, 1, 4, 2, 3, 2, 2, 1, 4, 4, 3, 3, 4, 4, 2, 4, 2, 3, 2, 2, 1, 4, 4, 5, 3, 4, 3, 3, 2, 4, 2, 3, 2, 2, 1, 8, 8, 5, 7, 3, 5, 3, 4, 2, 4, 2, 3, 2, 2, 1, 3, 3, 5, 2, 5, 2, 4, 2, 4, 2, 4, 2, 3, 2, 2, 1, 9, 9, 6, 7, 3, 7, 3, 4, 3, 4, 2, 4, 2, 3, 2, 2, 1

Offset: 3

Author

N. J. A. Sloane, Jun 17 2016

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) (with columns n >= 3 and k >= 2) begins as follows:
  1;
  1, 1;
  2, 2, 1;
  1, 1, 2, 1;
  3, 3, 2, 2, 1;
  2, 2, 2, 2, 2, 1;
  3, 3, 2, 3, 2, 2, 1;
  2, 2, 4, 1, 3, 2, 2, 1;
  5, 5, 3, 4, 2, 3, 2, 2, 1;
  2, 2, 2, 2, 3, 2, 3, 2, 2, 1;
  6, 6, 4, 5, 2, 4, 2, 3, 2, 2, 1;
  3, 3, 5, 3, 4, 1, 4, 2, 3, 2, 2, 1;
  4, 4, 3, 3, 4, 4, 2, 4, 2, 3, 2, 2, 1;
  ...
		

Links

• N. Benyahia Tani, S. Bouroubi, and O. Kihel, An effective approach for integer partitions using exactly two distinct sizes of parts, Bulletin du Laboratoire 03 (2015), 18-27.
• N. Benyahia Tani, S. Bouroubi, and O. Kihel, An effective approach for integer partitions using exactly two distinct sizes of parts, Elemente der Mathematik 72(2) (2017), 66-74.

Crossrefs

Row sums give A274108.

Cf. A002133, A117955, A117956, A216665.