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%I #6 Jun 25 2019 22:27:32
%S 0,0,0,1,5,18,56,160,432,1121,2827,6988,17052,41334,100082,243205,
%T 595313,1471278,3674756,9272410,23605202,60513201,155893167,402819550,
%U 1042358942,2697994240,6979913196,18041181065,46583002021,120161923640,309719942306
%N Number of Motzkin meanders of length n with an odd number of humps and without peaks.
%C 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.
%C A peak is an occurrence of the pattern UD.
%C A hump is an occurrence of the pattern UHH...HD (the number of Hs in the pattern is not fixed, and can be 0).
%H Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, <a href="https://lipn.univ-paris13.fr/~banderier/Papers/patterns2019.pdf">Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata</a>, Algorithmica (2019).
%F G.f.: (1/4)*(t^3-4*t^2+4*t-1+sqrt(t^6-4*t^5+4*t^4-2*t^3+4*t^2-4*t+1))/((-t^3+4*t^2-4*t+1)*t)-(1/4)*(-t^3-4*t^2+4*t-1+sqrt(t^6+4*t^5-4*t^4+2*t^3+4*t^2-4*t+1))/((t^3+4*t^2-4*t+1)*t).
%e For n = 4 the a(4) = 5 paths are UUHD, UHHD, UHDU, UHDH, HUHD.
%K nonn
%O 0,5
%A _Andrei Asinowski_, Jun 25 2019
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