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 A307557 Number of Motzkin meanders of length n with no level steps at odd level. 2
 1, 2, 4, 9, 20, 47, 110, 264, 634, 1541, 3754, 9204, 22622, 55817, 138026, 342203, 849984, 2115245, 5271970, 13158944, 32886338, 82285031, 206101422, 516728937, 1296664512, 3256472235, 8184526438, 20584627358, 51805243138, 130456806425, 328703655114 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A Motzkin meander is a lattice path with steps from the set {D=-1, H=0, U=1} that starts at (0,0), and never goes below the x-axis. LINKS Table of n, a(n) for n=0..30. Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata, Algorithmica (2019). FORMULA G.f.: ((1+t)/sqrt((t-1)*(4*t^2+t-1)) -1) / (2*t). D-finite with recurrence (n+1)*a(n) +(-n-2)*a(n-1) +(-5*n+3)*a(n-2) +(n+4)*a(n-3) +2*(2*n-5)*a(n-4)=0. - R. J. Mathar, Jan 25 2023 a(n) ~ sqrt(13 + 53/sqrt(17)) * (1 + sqrt(17))^n / (sqrt(Pi*n) * 2^(n + 3/2)). - Vaclav Kotesovec, Jun 24 2023 EXAMPLE For n = 3 the a(3) = 9 paths are UUU, UUH, UUD, UDU, UDH, HUU, HUD, HHU, HHH. CROSSREFS Cf. A307555. Sequence in context: A138164 A130802 A022543 * A036618 A349014 A003018 Adjacent sequences: A307554 A307555 A307556 * A307558 A307559 A307560 KEYWORD nonn AUTHOR Andrei Asinowski, Apr 14 2019 STATUS approved

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Last modified September 17 23:36 EDT 2024. Contains 375991 sequences. (Running on oeis4.)