

A259899


a(n) is the minimal position at which the maximal value of row n appears in row n of triangle A080936.


4



1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13
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OFFSET

1,3


COMMENTS

Empirical: for n>2 there is a unique position at which the maximum of row n occurs.
Conjecture: a(n) = floor(sqrt(p*n+q)+r) for all n>=1, where p = 2.67996... = A265179^2 and q,r are some constants (best values found: q=3.6, r=1).


LINKS

Gheorghe Coserea, Table of n, a(n) for n = 1..1535


FORMULA

a(n) = min argmax(k>T(n,k), k=1..n), that is a(n) = min{k, T(n,k) = max{T(n,p), p=1..n}}, where T(n,k) is the number of Dyck paths of length 2n and height k, 1 <= k <= n.
a(n) ~ K * sqrt(n), where K = 1.63706... (see A265179).  Gheorghe Coserea, Dec 05 2015


EXAMPLE

For n=2, a(2)=1 because max{T(2,p), p=1..2}=1 and T(2,1)=1.
For n=4, a(4)=2 because max{T(4,p), p=1..4}=7 and T(4,2)=7.
For n=16, a(16)=5 because max{T(16,p), p=1..16}=9246276 and T(16,5)=9246276.


CROSSREFS

Cf. A080936, A259885 (value of maximum), A265179.
Sequence in context: A143824 A182009 A034463 * A071996 A072747 A194295
Adjacent sequences: A259896 A259897 A259898 * A259900 A259901 A259902


KEYWORD

nonn,walk


AUTHOR

Gheorghe Coserea, Jul 07 2015


STATUS

approved



