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 A257519 Number of Motzkin paths of length n with no peaks at level 4. 1
 1, 1, 2, 4, 9, 21, 51, 127, 322, 827, 2145, 5607, 14751, 39020, 103713, 276848, 741901, 1995340, 5384554, 14576673, 39579527, 107776557, 294283193, 805649528, 2211176173, 6083560542, 16776970140, 46372110274, 128456563024, 356600559820, 991986172469, 2765030171165, 7722156349298, 21607098380159 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 FORMULA G.f.: 1/(1-x-x^2/(1-x-x^2/(1-x-x^2/(1-x+x^2*(1-M(x)))))), where M(x) is the g.f. of Motzkin numbers A001006. a(n) ~ 3^(n+7/2)/(98*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 27 2015 EXAMPLE For n=4 we have 9 paths: HHHH, UDUD, UHDH, HUHD, UHHD, UDHH, HUDH, HHUD and UUDD MATHEMATICA CoefficientList[Series[1/(1-x-x^2/(1-x-x^2/(1-x-x^2/(1-x+x^2*(1-(1-x-(1-2*x-3*x^2)^(1/2))/(2*x^2)))))), {x, 0, 30}], x] (* Vaclav Kotesovec, Apr 27 2015 *) PROG (PARI) x='x+O('x^50); Vec(1/(1-x-x^2/(1-x-x^2/(1-x-x^2/(1-x+x^2*(1-(1-x-(1-2*x-3*x^2)^(1/2))/(2*x^2))))))) \\ G. C. Greubel, Jun 03 2017 CROSSREFS Cf. A089372, A257300, A257104. Sequence in context: A051529 A230554 A005207 * A257387 A094286 A094287 Adjacent sequences:  A257516 A257517 A257518 * A257520 A257521 A257522 KEYWORD nonn AUTHOR José Luis Ramírez Ramírez, Apr 27 2015 STATUS approved

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Last modified August 19 03:31 EDT 2022. Contains 356216 sequences. (Running on oeis4.)