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A190163 Number of subwords of type dh^ju (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). 1
0, 0, 0, 0, 0, 0, 0, 1, 5, 18, 58, 174, 500, 1399, 3843, 10421, 27997, 74699, 198267, 524135, 1381261, 3631068, 9526568, 24954538, 65283648, 170610003, 445484163, 1162396269, 3031267533, 7901082379, 20586262763, 53620039074, 139624131310, 363495081689, 946147596489, 2462387385085 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

a(n)=Sum(k*A098083(n,k), k>=0).

LINKS

Table of n, a(n) for n=0..35.

FORMULA

G.f.: G(z)=z^5*g^2*(g-1)^2/[(1-z)(1-z^2*g^2)], where g=1+zg+z^2*g(g-1).

Conjecture D-finite with recurrence -4*(n+1)*(n-7)*a(n) +(13*n^2-85*n+28)*a(n-1) +(-7*n^2+52*n-41)*a(n-2) +(5*n^2-41*n+67)*a(n-3) +(-13*n^2+103*n-197)*a(n-4) +(7*n-29)*(n-5)*a(n-5) -(n-5)*(n-6)*a(n-6)=0. - R. J. Mathar, Jul 22 2022

EXAMPLE

a(7)=1 because among the 37 (=A004148(7)) peakless  Motzkin paths of length 7 only uh(dhu)hd  has a subword of the prescribed type (shown between parentheses).

MAPLE

eq := g = 1+z*g+z^2*g*(g-1): g := RootOf(eq, g): G := z^5*g^2*(g-1)^2/((1-z)*(1-z^2*g^2)): Gser := series(G, z = 0, 38): seq(coeff(Gser, z, n), n = 0 .. 35);

CROSSREFS

Cf. A098083, A004148

Sequence in context: A272583 A247717 A128553 * A335551 A235612 A000340

Adjacent sequences:  A190160 A190161 A190162 * A190164 A190165 A190166

KEYWORD

nonn

AUTHOR

Emeric Deutsch, May 05 2011

STATUS

approved

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Last modified August 15 20:27 EDT 2022. Contains 356148 sequences. (Running on oeis4.)