A120565 Maximum over all planar partitions of n of the number of ways the partition can be shrunk by removing a single element.

0, 1, 1, 2, 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13, 13, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 20, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24

Offset: 0

Author

Franklin T. Adams-Watters, Jun 14 2006

Keywords

• nonn

Comments

Maximum of any sum_i k_i, where sum_i k_i*(k_i+1)/2 <= n.

Crossrefs

Row lengths of A098529.

Formula

For n > 2, let m be the largest value such that tetrahedral number m*(m+1)*(m+2)/6 <= n. Then a(n) = max(m*(m+1)/2, m+1 + a(n - (m+1)*(m+2)/2)), taking a(k) to be 0 for k < 0.