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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 Table of n, a(n) for n=0..30. 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 Adjacent sequences: A329671 A329672 A329673 * A329675 A329676 A329677 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.)