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A025179 a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is an integer, s(0) = 0, |s(1)| = 1, |s(i) - s(i-1)| <= 1 for i >= 2, s(n) = 1. Also a(n) = T(n,n-1), where T is the array defined in A025177. 5
1, 4, 10, 29, 81, 231, 659, 1891, 5443, 15718, 45508, 132067, 384047, 1118820, 3264642, 9539787, 27913083, 81769236, 239794422, 703906719, 2068153899, 6081507831, 17896695831, 52703944965, 155310270101, 457956633826, 1351132539604 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 2..1000 (terms 2..200 from T. D. Noe)

FORMULA

Equals (1/2) * A024997(n+1).

From Vladeta Jovovic, Jan 01 2004: (Start)

a(n) = Sum_{k=0..floor(n/2)} binomial(n, 2*k)*binomial(2*k+1, k+1).

E.g.f.: exp(x)*(BesselI(0, 2*x)+BesselI(2, 2*x)). (End)

From Paul Barry, Sep 17 2005: (Start)

G.f.: ((1-x)^2 - (1-x)*sqrt(1-2*x-3*x^2))/(2*x*sqrt(1-2*x-3*x^2)).

a(n+1) = Sum_{k=0..n} C(n, k)*C(k+1, k/2+1)*(1+(-1)^k)/2}. (End)

Conjecture: (n+1)*a(n) +(-3*n+1)*a(n-1) +(-n-5)*a(n-2) +3*(n-3)*a(n-3)=0. - R. J. Mathar, Nov 26 2012

a(n) ~ 3^(n-1/2) / sqrt(Pi*n). - Vaclav Kotesovec, Feb 13 2014

MATHEMATICA

Rest[Rest[CoefficientList[Series[((1-x)^2-(1-x)*Sqrt[1-2*x-3*x^2]) /(2*x*Sqrt[1-2*x-3*x^2]), {x, 0, 20}], x]]] (* Vaclav Kotesovec, Feb 13 2014 *)

PROG

(PARI) x='x +O('x^50); Vec(((1-x)^2-(1-x +2*x^2)*sqrt(1-2*x-3*x^2)) /(2*x*sqrt(1 - 2*x -3*x^2))) \\ G. C. Greubel, Mar 01 2017

CROSSREFS

Cf. A024997, A026135.

Sequence in context: A329156 A052946 A026152 * A116388 A221420 A212262

Adjacent sequences:  A025176 A025177 A025178 * A025180 A025181 A025182

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified May 11 10:28 EDT 2021. Contains 343788 sequences. (Running on oeis4.)