A115724 Number of partitions with maximum rectangle n.

1, 1, 3, 5, 16, 16, 76, 53, 218, 303, 750, 412, 3680, 1361, 5015, 9206, 23162, 8290, 66166, 19936, 161656, 192181, 236007, 100730, 1338186, 819694, 1180478, 1924986, 5215844, 1246468, 17370367, 3098322, 24926724, 23473968, 24790503, 41886304, 227243488

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..100

Eric Weisstein's World of Mathematics, Ferrers Diagram.

Formula

a(n) = A115725(n) - A115725(n-1).

Example

The 16 partitions with maximum rectangle 4 are [4], [2^2], [1^4], [4,1], [3,2], [2^2,1], [2,1^3], [4,2], [4,1^2], [3,2,1], [3,1^3], [2^2,1^2], [4,2,1], [4,1^3], [3,2,1^2] and [4,2,1^2].

Crossrefs

Cf. A115725, A115723, A115726, A115727.

Sequence in context: A215444 A325257 A006593 * A039782 A331638 A080056

Adjacent sequences: A115721 A115722 A115723 * A115725 A115726 A115727

Keyword

nonn

Author

Franklin T. Adams-Watters, Mar 11 2006

Status

approved