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 A120565 Maximum over all planar partitions of n of the number of ways the partition can be shrunk by removing a single element. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Maximum of any sum_i k_i, where sum_i k_i*(k_i+1)/2 <= n. LINKS 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

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Last modified June 16 19:43 EDT 2019. Contains 324155 sequences. (Running on oeis4.)