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A329667 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UU and HH. 2
1, 2, 3, 6, 11, 21, 42, 83, 167, 341, 697, 1437, 2983, 6211, 12996, 27304, 57528, 121601, 257759, 547652, 1166299, 2489010, 5321780, 11398972, 24456235, 52549847, 113077188, 243645011, 525630690, 1135309380, 2454863253, 5313639848, 11512892983, 24967852309 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). A meander is a path starting at (0,0) and never crossing the x-axis, i.e. staying at nonnegative altitude.

LINKS

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

FORMULA

G.f.: (1/2)*(1-t^3-3*t^2-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))*(t+1)/((t^2+2*t-1)*t^2).

EXAMPLE

a(3)=6 since we have 6 meanders of length 3, namely UHU, UDU, UHD, UDH, HUH and HUD.

PROG

(PARI) my(t='t+O('t^40)); Vec((1/2)*(1-t^3-3*t^2-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))*(t+1)/((t^2+2*t-1)*t^2)) \\ Michel Marcus, Nov 25 2019

CROSSREFS

Cf. A329666 (excursions with same forbidden consecutive steps).

Sequence in context: A008930 A339151 A164362 * A026742 A316471 A018268

Adjacent sequences:  A329664 A329665 A329666 * A329668 A329669 A329670

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Nov 25 2019

STATUS

approved

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Last modified February 27 22:27 EST 2021. Contains 341693 sequences. (Running on oeis4.)