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
Examples
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; ...
Links
- Alois P. Heinz, Rows n = 1..141, flattened
- Eric Weisstein's World of Mathematics, Ferrers Diagram.
Crossrefs
Formula
Sum_{k=1..n} k * T(n,k) = A182099(n).
Comments