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A243754 Number of Dyck paths of semilength n avoiding the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

%I A243754 #7 Jun 10 2014 04:54:25
%S A243754 1,0,0,1,1,9,1,127,323,1515,4191,10455,20705,93802,113634,3219205,
%T A243754 10626023,45980364,139604903,555857157,1334821448,7577098816,
%U A243754 20676558270,61994003643,193904367362,800928670232,2374027931492,12506574770693,29311991924792
%N A243754 Number of Dyck paths of semilength n avoiding the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).
%H A243754 Alois P. Heinz, <a href="/A243754/b243754.txt">Table of n, a(n) for n = 0..512</a>
%e A243754 a(5) = 9 because there are 9 Dyck paths of semilength 5 avoiding the consecutive step pattern UDU given by the binary expansion of 5 = 101_2: UUDDUUDDUD, UUDDUUUDDD, UUUDDDUUDD, UUUDDUDDUD, UUUDDUUDDD, UUUUDDDDUD, UUUUDDDUDD, UUUUDDUDDD, UUUUUDDDDD.
%e A243754 a(6) = 1: UDUDUDUDUDUD.
%Y A243754 Column k=0 of A243752.
%Y A243754 Main diagonal of A243753.
%K A243754 nonn
%O A243754 0,6
%A A243754 _Alois P. Heinz_, Jun 09 2014