A061197 Table by antidiagonals T(n,k) of number of partitions of k where the largest part is less than or equal to n and where there are no more than two of any particular sized part.

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 0, 0, 1, 3, 2, 2, 1, 1, 0, 0, 1, 3, 4, 2, 2, 1, 1, 0, 0, 0, 3, 4, 4, 2, 2, 1, 1, 0, 0, 0, 3, 5, 5, 4, 2, 2, 1, 1, 0, 0, 0, 3, 5, 6, 5, 4, 2, 2, 1, 1, 0, 0, 0, 2, 7, 7, 7, 5, 4, 2, 2, 1, 1, 0, 0, 0, 2, 6, 9, 8, 7, 5, 4, 2, 2, 1, 1

Offset: 0

Author

Henry Bottomley, Apr 20 2001

Keywords

• nonn
• tabl

Examples

			Table begins:
  1, 0, 0, 0, 0, 0, ...,
  1, 1, 1, 0, 0, 0, ...,
  1, 1, 2, 1, 2, 1, ...,
  1, 1, 2, 2, 3, 3, ...,
  ...
T(3,5)=3 since 5 can be written as 3+2 or 3+1+1 or 2+2+1.
		

Crossrefs

Main diagonal is A000726.

Formula

T(n, k) = T(n-1, k) + T(n-1, k-n) + T(n-1, k-2*n) with T(0, 0)=1 and T(n, k)=0 if n or k are negative. [Corrected by Sean A. Irvine, Jan 24 2023]