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
KEYWORD
nonn,walk
AUTHOR
Gheorghe Coserea, Jul 07 2015
STATUS
approved