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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
OFFSET
0,2
COMMENTS
A partition has maximum rectangle <= n iff it is a subpartition of row n of A010766.
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved