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A060899 Number of walks of length n on square lattice, starting at origin, staying on points with x+y >= 0. 3
1, 2, 8, 24, 96, 320, 1280, 4480, 17920, 64512, 258048, 946176, 3784704, 14057472, 56229888, 210862080, 843448320, 3186360320, 12745441280, 48432676864, 193730707456, 739699064832, 2958796259328, 11342052327424 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,200

Paul Barry, The Central Coefficients of a Family of Pascal-like Triangles and Colored Lattice Paths, J. Int. Seq., Vol. 22 (2019), Article 19.1.3.

A. Bostan, Computer Algebra for Lattice Path Combinatorics, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.

FORMULA

a(n) = 2^n*binomial(n, [n/2]);

G.f.: (sqrt((1+4*x)/(1-4*x))-1)/4/x. - Vladeta Jovovic, Apr 28 2003

E.g.f.: BesselI(0, 4*x)+BesselI(1, 4*x). - Vladeta Jovovic, Apr 28 2003

a(n) = 4^n*sum{k=0..n, C(n,k)C(k)/(-2)^k}, with C(n)=A000108(n). - Paul Barry, Dec 28 2006

(n+1)*a(n) -4*a(n-1) +16*(-n+1)*a(n-2)=0. - R. J. Mathar, Nov 24 2012

a(n) = (-4)^n*hypergeom([3/2,-n],[2],2). - Peter Luschny, Apr 26 2016

MATHEMATICA

Table[2^n Binomial[n, Floor[n/2]], {n, 0, 30}] (* Harvey P. Dale, Oct 15 2017 *)

PROG

(PARI) { for (n=0, 200, write("b060899.txt", n, " ", 2^n*binomial(n, n\2)); ) } \\ Harry J. Smith, Jul 14 2009

CROSSREFS

Cf. A005566, A001700, A060897-A060900.

Cf. A001405.

Sequence in context: A007223 A106189 A106183 * A213951 A150665 A150666

Adjacent sequences:  A060896 A060897 A060898 * A060900 A060901 A060902

KEYWORD

nonn

AUTHOR

David W. Wilson, May 05 2001

STATUS

approved

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Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)