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A329693 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HH, HD and DU 2
1, 1, 1, 2, 2, 3, 4, 6, 9, 13, 21, 31, 50, 78, 123, 200, 315, 517, 831, 1355, 2224, 3620, 5995, 9835, 16291, 27004, 44734, 74625, 124078, 207437, 346765, 580418, 974358, 1634622, 2750502, 4628758, 7800544, 13164287, 22223486, 37579843, 63571333, 107659948, 182479796, 309478532 (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..43.

FORMULA

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

EXAMPLE

a(5)=3 since we have 3 excursions of length 5, namely UUDDH, HUUDD and UDHUD.

CROSSREFS

Cf. A329691, A329692.

Sequence in context: A212264 A174650 A107293 * A329976 A329703 A001611

Adjacent sequences:  A329690 A329691 A329692 * A329694 A329695 A329696

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Dec 06 2019

STATUS

approved

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Last modified September 19 11:23 EDT 2021. Contains 347556 sequences. (Running on oeis4.)