login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A115725 Number of partitions with maximum rectangle <= n. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A002094 A212709 A264867 * A305577 A196630 A079572

Adjacent sequences:  A115722 A115723 A115724 * A115726 A115727 A115728

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Mar 11 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 5 04:05 EDT 2020. Contains 335459 sequences. (Running on oeis4.)