A243772 - OEIS

A243772

Number of Dyck paths of semilength n having exactly three (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

%I #6 Jun 11 2014 22:05:53

%S 4,5,35,0,280,1991,4115,34840,96286,309036,1045200,193240,5159120,

%T 40653929,105545340,603157520,2582073261,11015773404,26828044860,

%U 182118031760,726122370210,3026319516720,9620891607824,49247195403600,161316665871200,638742288482240

%N Number of Dyck paths of semilength n having exactly three (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

%H Alois P. Heinz, <a href="/A243772/b243772.txt">Table of n, a(n) for n = 5..200</a>

%e a(5) = 4: UDUDUDUUDD, UDUDUUDUDD, UDUUDUDUDD, UUDUDUDUDD.

%e a(6) = 5: UUDDUUDDUUDD, UUDDUUDUUDDD, UUDUUDDDUUDD, UUDUUDDUUDDD, UUDUUDUUDDDD.

%Y Column k=3 of A243752.

%Y Main diagonal of A243829.

%K nonn

%O 5,1

%A _Alois P. Heinz_, Jun 10 2014