A151340 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (0, 1), (1, -1), (1, 0)}.

1, 0, 0, 2, 4, 8, 28, 108, 372, 1280, 4776, 18464, 71840, 282856, 1134696, 4623328, 19044552, 79217024, 332678424, 1409411128, 6017276432, 25869106896, 111931476168, 487189405200, 2132112963608, 9377901602688, 41440635484904, 183921242382848, 819585479873264, 3666044711577832

Offset

0,4

References

Alin Bostan, Calcul Formel pour la Combinatoire des Marches [The text is in English], Habilitation à Diriger des Recherches, Laboratoire d’Informatique de Paris Nord, Université Paris 13, December 2017; https://specfun.inria.fr/bostan/HDR.pdf

Links

Table of n, a(n) for n=0..29.

A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 40, Tag 42.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]

Crossrefs

Sequence in context: A219969 A034919 A298682 * A134316 A049461 A103791

Adjacent sequences: A151337 A151338 A151339 * A151341 A151342 A151343

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved