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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 A243774 #6 Jun 11 2014 22:11:00
%S A243774 1,0,0,244,1,246,379,0,179790,0,5096,1721037,1595288,3992352,
%T A243774 455454822,842632268,63280332,4243256192,50749141182,109671572304,
%U A243774 614565138768,2580550363440,2759439518892,4369338844416,474848703434955,110506726968,50798936389648
%N 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).
%H A243774 Alois P. Heinz, <a href="/A243774/b243774.txt">Table of n, a(n) for n = 7..200</a>
%e A243774 a(7) = 1: UUUUUUUDDDDDDD.
%e A243774 a(11) = 1: UDUUDUUDUUDUUDUUDDDDDD.
%Y A243774 Column k=5 of A243752.
%Y A243774 Main diagonal of A243831.
%K A243774 nonn
%O A243774 7,4
%A A243774 _Alois P. Heinz_, Jun 10 2014