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 A257387 Number of Motzkin paths of length n with no level steps at height 4. 1
 1, 1, 2, 4, 9, 21, 51, 127, 323, 834, 2179, 5743, 15238, 40637, 108800, 292200, 786703, 2122387, 5735596, 15522682, 42064028, 114117541, 309918698, 842489130, 2292332265, 6242655886 (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 a(n) = a(n-1) + Sum_{j=0..n-2} A257386(j)*a(n-j). G.f: 1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*R(x)))))))), where R(x) is the g.f. of Riordan numbers (A005043). a(n) ~ 3^(n+1/2)/(24*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Apr 24 2015 MATHEMATICA CoefficientList[Series[1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1+x-Sqrt[1-2*x-3*x^2])/(2*x*(1+x))))))))), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 24 2015 *) PROG (PARI) x='x+O('x^50); Vec(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)))))))))) \\ G. C. Greubel, Jun 03 2017 CROSSREFS Cf. A005043, A217312, A252354, A257386. Sequence in context: A230554 A005207 A257519 * A094286 A094287 A094288 Adjacent sequences: A257384 A257385 A257386 * A257388 A257389 A257390 KEYWORD nonn AUTHOR José Luis Ramírez Ramírez, Apr 21 2015 STATUS approved

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Last modified June 21 07:35 EDT 2024. Contains 373540 sequences. (Running on oeis4.)