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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
1, 1, 1, 2, 4, 8, 17, 36, 77, 167, 365, 805, 1790, 4008, 9033, 20477, 46663, 106843, 245691, 567194, 1314086, 3054442, 7120951, 16647056, 39015476, 91654385, 215780420, 509033640, 1203085539, 2848445175, 6755095119, 16044373511, 38162885226, 90897048648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..33.

FORMULA

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

EXAMPLE

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).

MAPLE

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);

CROSSREFS

Cf. A098083, A004148

Sequence in context: A226729 A063457 A262735 * A275691 A251691 A157904

Adjacent sequences:  A190159 A190160 A190161 * A190163 A190164 A190165

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 05 2011

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)