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A329674 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps DD. 2
1, 2, 5, 13, 34, 90, 240, 643, 1729, 4662, 12597, 34095, 92406, 250719, 680877, 1850457, 5032296, 13692674, 37274438, 101509476, 276535824, 753574253, 2054064713, 5600176231, 15271331416, 41651397245, 113618996429, 309979833301, 845805408448, 2308108658854, 6299205562846 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). A meander is a path starting at (0,0) and never crossing the x-axis, i.e., staying at nonnegative altitude.
LINKS
FORMULA
G.f.: -(1-3*t-t^2-sqrt(1-2*t-t^2-2*t^3+t^4))/(2*t*(1-2*t-2*t^2)).
D-finite with recurrence (n+1)*a(n) +(-4*n-1)*a(n-1) +(n-2)*a(n-2) +(4*n+1)*a(n-3) +(7*n-23)*a(n-4) +2*(n-2)*a(n-5) +2*(-n+5)*a(n-6)=0. - R. J. Mathar, Jan 25 2023
EXAMPLE
a(2)=5 since we have 5 meanders of length 2 avoiding DD, namely UU, UH, UD, HU and HH.
CROSSREFS
Cf. A004148 (shifted by 1) which counts excursions avoiding consecutive DD steps.
Cf. A329672 and A329673 which count meanders avoiding consecutive UU or HH respectively.
Sequence in context: A097417 A367657 A006801 * A114173 A238435 A023425
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Nov 26 2019
STATUS
approved

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Last modified May 26 03:59 EDT 2024. Contains 372807 sequences. (Running on oeis4.)