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%I #4 Mar 30 2012 17:36:27
%S 0,0,0,0,0,0,2,10,34,104,300,834,2270,6094,16206,42818,112606,295138,
%T 771616,2013550,5246954,13657882,35522364,92331014,239875614,
%U 622971814,1617463986,4198716114,10897812738,28282859174,73398069768,190474295608,494298218888,1282776917922
%N Number of subwords of type uh^ju and dh^jd (j>=1), where u=(1,1), h=(1,0), and d=(1,-1), in all peakless Motzkin paths of length n (can be easily expressed using RNA secondary structure terminology).
%C a(n)=Sum(k*A097100(n,k), k>=0).
%F G.f.: G(z)=2z^3*g^3*(g-1)/[(1-z)(1-z^2*g^2)], where g=1+zg+z^2*g(g-1).
%e a(6)=2 because among the 17 (=A004148(6)) peakless Motzkin paths of length 6 only (uhu)hdd and uuh(dhd) have subwords of the prescribed type (shown between parentheses).
%p eq := g = 1+z*g+z^2*g*(g-1): g := RootOf(eq, g): gser := series(2*z^5*g^3*(g-1)/((1-z)*(1-z^2*g^2)), z = 0, 38): seq(coeff(gser, z, n), n = 0 .. 33);
%Y Cf. A097100, A004148
%K nonn
%O 0,7
%A _Emeric Deutsch_, May 05 2011
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