A243774 - OEIS

A243774

Number of Dyck paths of semilength n having exactly five (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 22:11:00

%S 1,0,0,244,1,246,379,0,179790,0,5096,1721037,1595288,3992352,

%T 455454822,842632268,63280332,4243256192,50749141182,109671572304,

%U 614565138768,2580550363440,2759439518892,4369338844416,474848703434955,110506726968,50798936389648

%N Number of Dyck paths of semilength n having exactly five (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="/A243774/b243774.txt">Table of n, a(n) for n = 7..200</a>

%e a(7) = 1: UUUUUUUDDDDDDD.

%e a(11) = 1: UDUUDUUDUUDUUDUUDDDDDD.

%Y Column k=5 of A243752.

%Y Main diagonal of A243831.

%K nonn

%O 7,4

%A _Alois P. Heinz_, Jun 10 2014