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A120565
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Maximum over all planar partitions of n of the number of ways the partition can be shrunk by removing a single element.
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1
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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; internal format)
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OFFSET
| 0,4
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COMMENTS
| Maximum of any sum_i k_i, where sum_i k_i*(k_i+1)/2 <= n.
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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.
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CROSSREFS
| Row lengths of A098529.
Sequence in context: A087823 A037037 A156262 * A194198 A189674 A156250
Adjacent sequences: A120562 A120563 A120564 * A120566 A120567 A120568
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KEYWORD
| nonn
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 14 2006
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