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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
OFFSET
0,4
COMMENTS
Maximum of any sum_i k_i, where sum_i k_i*(k_i+1)/2 <= n.
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
KEYWORD
nonn
AUTHOR
STATUS
approved