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A329664 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU. 1
1, 1, 0, 1, 2, 2, 4, 8, 12, 21, 40, 69, 122, 227, 412, 747, 1386, 2567, 4744, 8851, 16566, 31004, 58268, 109858, 207368, 392331, 744072, 1413291, 2688822, 5124738, 9781492, 18694896, 35780444, 68566567, 131546440, 252661515, 485806614, 935017790, 1801327884, 3473467328, 6703610548 (list; graph; refs; listen; history; text; internal format)
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 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..40.

FORMULA

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

EXAMPLE

a(4)=2 as one has 2 excursions of length 4, namely: HUHD and UHDH.

CROSSREFS

Cf. A004149 (avoiding UD and DU).

Cf. A329666, A329665.

Sequence in context: A104221 A078044 A348851 * A153993 A244781 A052907

Adjacent sequences:  A329661 A329662 A329663 * A329665 A329666 A329667

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Nov 19 2019

STATUS

approved

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Last modified August 14 15:34 EDT 2022. Contains 356122 sequences. (Running on oeis4.)