

A329699


Number of excursions of length n with Motzkinsteps avoiding the consecutive steps UH, HU and HH.


1



1, 1, 1, 1, 2, 3, 6, 10, 20, 36, 72, 136, 273, 532, 1074, 2137, 4342, 8766, 17925, 36574, 75234, 154749, 320038, 662490, 1376653, 2864534, 5977603, 12492157, 26165052, 54882573, 115329739, 242683876, 511456452, 1079252975, 2280413318, 4823955728, 10216401353, 21659426346
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OFFSET

0,5


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 xaxis, i.e., staying at nonnegative altitude.


LINKS



FORMULA

G.f.: (1+t^3sqrt(14t^22t^3+t^6))/(2t^2).
G.f. A(x) satisfies: A(x) = x + 1 / (1  x^2 * A(x)).  Ilya Gutkovskiy, Nov 03 2021


EXAMPLE

a(5)=3 since we have the following 3 excursions of length 5: UUDDH, UUHDH and UDUDH.


CROSSREFS



KEYWORD

nonn,walk


AUTHOR



STATUS

approved



