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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
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.
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).
Sequence in context: A104221 A078044 A348851 * A153993 A244781 A052907
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Nov 19 2019
STATUS
approved