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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
 0, 0, 0, 1, 3, 7, 17, 41, 99, 242, 596, 1477, 3681, 9215, 23155, 58368, 147530, 373768, 948882, 2413264, 6147414, 15682008, 40056238, 102434119, 262228051, 671945055, 1723350315, 4423518544, 11362907022, 29208834520, 75131251334, 193370093508, 497969663062 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Same as A089742 except for the first three terms. - Georg Fischer, Oct 14 2018 LINKS FORMULA G.f.: z^3*G^2/((1-z)*(1-z^2*G^2)), where G = 1+z*G+z^2*G*(G-1). a(n) = Sum_{k>=0} k*A089741(n,k). EXAMPLE a(4)=3 because in HHHH, HUHD, UHDH and UHHD we have 0+1+1+1 subwords of the type UH^jD. MAPLE 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); CROSSREFS Cf. A004148, A089741, A089742. Sequence in context: A001333 A078057 A089742 * A131721 A259855 A058351 Adjacent sequences:  A187255 A187256 A187257 * A187259 A187260 A187261 KEYWORD nonn AUTHOR Emeric Deutsch, May 05 2011 STATUS approved

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Last modified June 13 12:44 EDT 2021. Contains 344996 sequences. (Running on oeis4.)