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

0,4

Comments

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

Links

Table of n, a(n) for n=0..75.

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.

Crossrefs

Row lengths of A098529.

Sequence in context: A156262 A218447 A305845 * A244989 A296021 A267097

Adjacent sequences: A120562 A120563 A120564 * A120566 A120567 A120568

Keyword

nonn

Author

Franklin T. Adams-Watters, Jun 14 2006

Status

approved