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

0,13

Links

Table of n, a(n) for n=0..104.

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]

Example

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.

Sequence in context: A249609 A232442 A107110 * A196346 A261884 A035178

Adjacent sequences: A061194 A061195 A061196 * A061198 A061199 A061200

Keyword

nonn,tabl

Author

Henry Bottomley, Apr 20 2001

Status

approved