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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 A243772 #6 Jun 11 2014 22:05:53
%S A243772 4,5,35,0,280,1991,4115,34840,96286,309036,1045200,193240,5159120,
%T A243772 40653929,105545340,603157520,2582073261,11015773404,26828044860,
%U A243772 182118031760,726122370210,3026319516720,9620891607824,49247195403600,161316665871200,638742288482240
%N 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).
%H A243772 Alois P. Heinz, <a href="/A243772/b243772.txt">Table of n, a(n) for n = 5..200</a>
%e A243772 a(5) = 4: UDUDUDUUDD, UDUDUUDUDD, UDUUDUDUDD, UUDUDUDUDD.
%e A243772 a(6) = 5: UUDDUUDDUUDD, UUDDUUDUUDDD, UUDUUDDDUUDD, UUDUUDDUUDDD, UUDUUDUUDDDD.
%Y A243772 Column k=3 of A243752.
%Y A243772 Main diagonal of A243829.
%K A243772 nonn
%O A243772 5,1
%A A243772 _Alois P. Heinz_, Jun 10 2014