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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
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
Sequence in context: A051529 A230554 A005207 * A257387 A094286 A094287
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)