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A187258 Number of UH^jD's for some j>0, in all peakless Motzkin paths of length n (here U=(1,1), D=(1,-1) and H=(1,0); can be easily expressed using RNA secondary structure terminology). 0

%I

%S 0,0,0,1,3,7,17,41,99,242,596,1477,3681,9215,23155,58368,147530,

%T 373768,948882,2413264,6147414,15682008,40056238,102434119,262228051,

%U 671945055,1723350315,4423518544,11362907022,29208834520,75131251334,193370093508,497969663062

%N Number of UH^jD's for some j>0, in all peakless Motzkin paths of length n (here U=(1,1), D=(1,-1) and H=(1,0); can be easily expressed using RNA secondary structure terminology).

%C Same as A089742 except for the first three terms. - _Georg Fischer_, Oct 14 2018

%F G.f.: z^3*G^2/((1-z)*(1-z^2*G^2)), where G = 1+z*G+z^2*G*(G-1).

%F a(n) = Sum_{k>=0} k*A089741(n,k).

%e a(4)=3 because in HHHH, HUHD, UHDH and UHHD we have 0+1+1+1 subwords of the type UH^jD.

%p eq := g = 1+z*g+z^2*g*(g-1): G := RootOf(eq, g): Gser := series(z^3*G^2/((1-z)*(1-z^2*G^2)), z = 0, 35): seq(coeff(Gser, z, n), n = 0 .. 32);

%Y Cf. A004148, A089741, A089742.

%K nonn

%O 0,5

%A _Emeric Deutsch_, May 05 2011

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Last modified August 2 15:51 EDT 2021. Contains 346428 sequences. (Running on oeis4.)