A151318 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, 1), (1, 0), (1, 1)}

1, 3, 13, 55, 249, 1131, 5253, 24543, 115825, 549331, 2620029, 12543367, 60270697, 290423355, 1403088885, 6793370415, 32956254945, 160152588195, 779470975725, 3798948989655, 18538237315545, 90565618791435, 442899758973285, 2167985089576575, 10621425660150609, 52078139149834611, 255533719072119133

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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

Alin Bostan, Andrew Elvey Price, Anthony John Guttmann, Jean-Marie Maillard, Stieltjes moment sequences for pattern-avoiding permutations, arXiv:2001.00393 [math.CO], 2020.

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

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

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, -1 + j, -1 + n] + aux[-1 + i, j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A183804 A117376 A264037 * A151212 A151213 A102287

Adjacent sequences: A151315 A151316 A151317 * A151319 A151320 A151321

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved