cp's OEIS Frontend

A187257 Number of UH^jU's for some j>0, where U=(1,1) and H=(1,1), in all peakless Motzkin paths of length n (can be easily expressed using RNA secondary structure terminology).

%I A187257 #6 Jul 15 2025 16:40:45
%S A187257 0,0,0,0,0,0,1,5,17,52,150,417,1135,3047,8103,21409,56303,147569,
%T A187257 385808,1006775,2623477,6828941,17761182,46165507,119937807,311485907,
%U A187257 808731993,2099358057,5448906369,14141429587,36699034884,95237147804,247149109444,641388458961
%N A187257 Number of UH^jU's for some j>0, where U=(1,1) and H=(1,1), in all peakless Motzkin paths of length n (can be easily expressed using RNA secondary structure terminology).
%C A187257 a(n)=Sum(k*A097777(n,k), k>=0).
%F A187257 G.f.=z^5*g^3*(g-1)/[(1-z)(1-z^2*g^2)], where g=1+zg+z^2*g(g-1)=A004148.
%e A187257 a(6)=1 because among the 17 (=A004148(6)) peakless Motzkin paths of length 6 only UHUHDD contains subwords of type UH^jU for some j>0 (here D=(1,-1)).
%Y A187257 Cf. A097777, A004148
%K A187257 nonn
%O A187257 0,8
%A A187257 _Emeric Deutsch_, May 05 2011