A115723 Table of partitions of n with maximum rectangle k.

1, 0, 2, 0, 1, 2, 0, 0, 2, 3, 0, 0, 1, 4, 2, 0, 0, 0, 5, 2, 4, 0, 0, 0, 3, 4, 6, 2, 0, 0, 0, 1, 4, 11, 2, 4, 0, 0, 0, 0, 3, 14, 4, 6, 3, 0, 0, 0, 0, 1, 15, 6, 12, 4, 4, 0, 0, 0, 0, 0, 13, 8, 18, 9, 6, 2, 0, 0, 0, 0, 0, 8, 10, 25, 14, 12, 2, 6, 0, 0, 0, 0, 0, 4, 9, 30, 22, 20, 4, 10, 2

Offset

1,3

Comments

T(n,k)=0 if n > A006218(k).

Links

Alois P. Heinz, Rows n = 1..141, flattened

Eric Weisstein's World of Mathematics, Ferrers Diagram.

Formula

Sum_{k=1..n} k * T(n,k) = A182099(n).

Example

The table starts:
  1;
  0, 2;
  0, 1, 2;
  0, 0, 2, 3;
  0, 0, 1, 4, 2;
  0, 0, 0, 5, 2,  4;
  0, 0, 0, 3, 4,  6, 2;
  0, 0, 0, 1, 4, 11, 2,  4;
  0, 0, 0, 0, 3, 14, 4,  6, 3;
  0, 0, 0, 0, 1, 15, 6, 12, 4, 4;
  ...

Crossrefs

Cf. A000005 (diagonal), A000041 (row sums), A061017 (column indices of leftmost nonzero elements), A115724 (column sums), A115727, A115728, A006218, A182099.

Sequence in context: A261249 A058650 A112177 * A238160 A178524 A321731

Adjacent sequences: A115720 A115721 A115722 * A115724 A115725 A115726

Keyword

nonn,tabl,look

Author

Franklin T. Adams-Watters, Mar 11 2006

Status

approved