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A329694 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH and DU. 1
1, 1, 1, 3, 3, 3, 8, 12, 13, 27, 50, 64, 109, 215, 322, 504, 966, 1616, 2526, 4578, 8115, 13143, 22836, 41162, 69410, 118536, 212498, 369226, 631631, 1119755, 1977612, 3419130, 6014450, 10684128, 18689970, 32807722, 58300072, 102905556, 181031164, 321348824, 570303658, 1007402762 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..41.

FORMULA

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

EXAMPLE

a(4)=3 since we have the following 3 excursions of length 4: UHDH, HUHD and HUDH.

CROSSREFS

Cf. A248100.

Sequence in context: A346159 A241739 A226509 * A183389 A275530 A180637

Adjacent sequences:  A329691 A329692 A329693 * A329695 A329696 A329697

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Dec 06 2019

STATUS

approved

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Last modified September 17 03:42 EDT 2021. Contains 347478 sequences. (Running on oeis4.)