A115725 Number of partitions with maximum rectangle <= n.

1, 2, 5, 10, 26, 42, 118, 171, 389, 692, 1442, 1854, 5534, 6895, 11910, 21116, 44278, 52568, 118734, 138670, 300326, 492507, 728514, 829244, 2167430, 2987124, 4167602, 6092588, 11308432, 12554900, 29925267, 33023589, 57950313, 81424281, 106214784, 148101088

Offset

0,2

Comments

A partition has maximum rectangle <= n iff it is a subpartition of row n of A010766.

Links

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

Eric Weisstein's World of Mathematics, Ferrers Diagram.

Formula

a(n) = subpart([<floor(n/k)]). The subpart function is A115728 (or A115729), [<floor(n/k)>] is row n of A010766.

a(n) = Sum_{k>=0} A182114(k,n). - Alois P. Heinz, Nov 02 2012

Example

The 10 partitions with maximum rectangle <= 3: 0: []; 1: [1]; 2: [2], [1^2], [2,1]; 3: [3], [1^3], [3,1], [2,1^2], [3,1^2].

Crossrefs

Cf. A115728, A115729, A115724, A010766.

Sequence in context: A212709 A264867 A354832 * A305577 A196630 A079572

Adjacent sequences: A115722 A115723 A115724 * A115726 A115727 A115728

Keyword

nonn

Author

Franklin T. Adams-Watters, Mar 11 2006

Status

approved