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 A329690 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH, DU and DD. 0
 1, 1, 1, 3, 3, 2, 5, 9, 8, 10, 23, 32, 32, 56, 106, 131, 164, 310, 499, 617, 932, 1682, 2451, 3269, 5426, 9067, 12757, 18650, 31507, 49381, 70446, 110111, 182073, 275332, 407683, 657438, 1053990, 1581022, 2430364, 3935375, 6159050, 9334508, 14715327, 23606027, 36518354, 56308374 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). An excursion is a path starting at (0,0), ending at (n,0) and never crossing the x-axis, i.e., staying at nonnegative altitude. LINKS Table of n, a(n) for n=0..45. FORMULA G.f.: ((1+t)(1+t-t^3-3t^4-(1+t)*sqrt(1-2t^3-4t^4+t^6)))/(2t^5). D-finite with recurrence: (n+5)*a(n) -2*a(n-1) +2*(1)*a(n-2) +(-2*n-3)*a(n-3) +2*(-2*n+5)*a(n-4) +2*a(n-5) +(n-6)*a(n-6)=0. - R. J. Mathar, Jan 27 2020 EXAMPLE a(4)=3 because we have 3 such excursions of length 4, namely UHDH, HUHD and HUDH. CROSSREFS Cf. 329689. Sequence in context: A359484 A186111 A186813 * A293521 A285443 A110898 Adjacent sequences: A329687 A329688 A329689 * A329691 A329692 A329693 KEYWORD nonn,walk AUTHOR Valerie Roitner, Dec 06 2019 STATUS approved

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Last modified October 1 18:47 EDT 2023. Contains 365828 sequences. (Running on oeis4.)