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A057648 Number of excursions of length n on the upper-right part of the honeycomb lattice. 1
1, 0, 2, 2, 13, 34, 158, 594, 2665, 11558, 53320, 247488, 1181266, 5708884, 28049474, 139417402, 701063005, 3559326294, 18233244530, 94140532624, 489573775236, 2562613997512, 13493827469116, 71441865994904 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Excursions = walks from the origin to the origin.

LINKS

Robert Israel, Table of n, a(n) for n = 0..1000

C. Banderier, Analytic combinatorics of random walks and planar maps, PhD Thesis, 2001.

FORMULA

G.f.: (1-2*x)*hypergeom([-1/2, 1/2],[2],16*x^2/(1-2*x)^2)/(4*x^2) - (2*x+1)*((1-6*x)*hypergeom([1/3, 2/3],[2],27*x^2*(2*x+1))+1/2)/(6*x^2).  - Mark van Hoeij, Dec 08 2014

MAPLE

gf:=(1-2*x)*hypergeom([-1/2, 1/2], [2], 16*x^2/(1-2*x)^2)/(4*x^2) - (2*x+1)*((1-6*x)*hypergeom([1/3, 2/3], [2], 27*x^2*(2*x+1))+1/2)/(6*x^2):

S:= series(gf, x, 103):

seq(coeff(S, x, j), j=0..100); # Robert Israel, Dec 08 2014

CROSSREFS

Sequence in context: A155915 A173466 A151367 * A282460 A327930 A068511

Adjacent sequences:  A057645 A057646 A057647 * A057649 A057650 A057651

KEYWORD

nonn

AUTHOR

Cyril Banderier, Oct 12 2000

STATUS

approved

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Last modified May 25 20:58 EDT 2020. Contains 334597 sequences. (Running on oeis4.)