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A243773 Number of Dyck paths of semilength n having exactly four (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 A243773 #5 Jun 11 2014 22:08:22
%S A243773 1,0,7,0,14,781,220,5685,12104,10920,471900,140,402920,10257990,
%T A243773 17056745,82403580,1152019163,3595341849,2413091295,40392418220,
%U A243773 235442534915,804119873760,2973203848860,15274217567340,32286978092250,94142466440960,909684828893676
%N A243773 Number of Dyck paths of semilength n having exactly four (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 A243773 Alois P. Heinz, <a href="/A243773/b243773.txt">Table of n, a(n) for n = 5..200</a>
%e A243773 a(5) = 1: UDUDUDUDUD.
%e A243773 a(7) = 7: UDUUUUUUDDDDDD, UUUUUUDDDDDDUD, UUUUUUDDDDDUDD, UUUUUUDDDDUDDD, UUUUUUDDDUDDDD, UUUUUUDDUDDDDD, UUUUUUDUDDDDDD.
%Y A243773 Column k=4 of A243752.
%Y A243773 Main diagonal of A243830.
%K A243773 nonn
%O A243773 5,3
%A A243773 _Alois P. Heinz_, Jun 10 2014