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A329688 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH, HD and DU. 0
1, 1, 1, 2, 1, 2, 4, 2, 5, 10, 5, 14, 28, 14, 42, 84, 42, 132, 264, 132, 429, 858, 429, 1430, 2860, 1430, 4862, 9724, 4862, 16796, 33592, 16796, 58786, 117572, 58786, 208012, 416024, 208012, 742900, 1485800, 742900, 2674440, 5348880, 2674440, 9694845, 19389690, 9694845, 35357670 (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 on the x-axis and never crossing the x-axis, i.e., staying at nonnegative altitude.

LINKS

Table of n, a(n) for n=0..47.

FORMULA

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

Conjecture D-finite with recurrence: -(n+4)*(5*n^2-11*n-6)*a(n) +36*(-n+1)*a(n-1) +36*(n-2)*a(n-2) +2*(2*n-5)*(5*n^2-n-12)*a(n-3)=0. - R. J. Mathar, Jan 09 2020

EXAMPLE

a(5)=2 since we have 2 such excursions of length 5, namely UHUDD and UDHUD.

CROSSREFS

Cf. A000108.

Sequence in context: A060547 A079878 A324469 * A217920 A137406 A181293

Adjacent sequences:  A329685 A329686 A329687 * A329689 A329690 A329691

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Nov 29 2019

STATUS

approved

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Last modified September 26 02:27 EDT 2021. Contains 347664 sequences. (Running on oeis4.)