

A329674


Number of meanders of length n with Motzkinsteps 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
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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 xaxis, i.e., staying at nonnegative altitude.


LINKS



FORMULA

G.f.: (13*tt^2sqrt(12*tt^22*t^3+t^4))/(2*t*(12*t2*t^2)).
Dfinite with recurrence (n+1)*a(n) +(4*n1)*a(n1) +(n2)*a(n2) +(4*n+1)*a(n3) +(7*n23)*a(n4) +2*(n2)*a(n5) +2*(n+5)*a(n6)=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.


KEYWORD

nonn,walk


AUTHOR



STATUS

approved



