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A190162 Number of peakless Motzkin paths of length n containing no subwords of  type dh^ju (j>=1), where u=(1,1), h=(1,0), and d=(1,-1) (can be easily expressed using RNA secondary structure terminology). 1

%I

%S 1,1,1,2,4,8,17,36,77,167,365,805,1790,4008,9033,20477,46663,106843,

%T 245691,567194,1314086,3054442,7120951,16647056,39015476,91654385,

%U 215780420,509033640,1203085539,2848445175,6755095119,16044373511,38162885226,90897048648

%N Number of peakless Motzkin paths of length n containing no subwords of type dh^ju (j>=1), where u=(1,1), h=(1,0), and d=(1,-1) (can be easily expressed using RNA secondary structure terminology).

%C a(n)=A098083(n,0).

%F G.f.: G=G(z) satisfies the equation G=1+zG+z^2*(G-1)[(1-z)G+z/(1-z)].

%e a(7)=36 because among the 37 (=A004148(7)) peakless Motzkin paths of length 7 only uh(dhu)hd has a subword of the forbidden type (shown between parentheses).

%p eq := G = 1+z*G+z^2*(G-1)*((1-z)*G+z/(1-z)): G := RootOf(eq,G): Gser := series(G,z=0,38): seq(coeff(Gser,z,n), n = 0 .. 33);

%Y Cf. A098083, A004148

%K nonn

%O 0,4

%A _Emeric Deutsch_, May 05 2011

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Last modified June 25 03:30 EDT 2021. Contains 345449 sequences. (Running on oeis4.)