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 A347036 Number of Motzkin paths of length n avoiding UHHD. 0
 1, 1, 2, 4, 8, 18, 33, 73, 127, 279, 473, 1045, 1749, 3905, 6490, 14652, 24244, 55286, 91190, 209748, 345102, 799580, 1312844, 3060614, 5016396, 11756454, 19239412, 45294870, 74024768, 174964546, 285599169, 677384297, 1104527095, 2627757663, 4280633021, 10211786449 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..35. Christian Bean, Antonio Bernini, Matteo Cervetti and Luca Ferrari, Pattern avoiding Motzkin paths are almost rational, arXiv:2108.03037 [math.CO], 2021. FORMULA G.f.: (1-3*x-4*x^2+12*x^3 - (1-3*x-4*x^2+8*x^3)*sqrt(1-4*x^2))/(2*x^2*(1-2*x-3*x^2+8*x^3-4*x^4)). D-finite with recurrence -(n+2)*(87*n-587)*a(n) +2*(262*n^2-1391*n-1316)*a(n-1) +(-439*n^2+2325*n+3238)*a(n-2) +6*(-291*n^2+1878*n-3058)*a(n-3) +4*(787*n^2-5112*n+7910)*a(n-4) -8*(n-3)*(175*n-628)*a(n-5)=0. - R. J. Mathar, Mar 06 2022 PROG (PARI) my(x='x+O('x^40)); Vec((1-3*x-4*x^2+12*x^3 - (1-3*x-4*x^2+8*x^3)*sqrt(1-4*x^2))/(2*x^2*(1-2*x-3*x^2+8*x^3-4*x^4))) CROSSREFS Cf. A001006. Sequence in context: A229718 A246469 A092507 * A297188 A291583 A218874 Adjacent sequences: A347033 A347034 A347035 * A347037 A347038 A347039 KEYWORD nonn,easy AUTHOR Michel Marcus, Aug 12 2021 STATUS approved

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Last modified November 28 14:45 EST 2023. Contains 367419 sequences. (Running on oeis4.)