A151299 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), (0, 1), (1, 1)}.

1, 2, 8, 28, 116, 465, 1980, 8393, 36495, 159224, 703466, 3122910, 13965291, 62727001, 283127006, 1282634921, 5831588809, 26593352814, 121612750646, 557511728992, 2561633569528, 11794202901847, 54405218589731, 251397920522538, 1163526932180757, 5393008739923600, 25031149678866730, 116327793681728800

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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

Crossrefs

Sequence in context: A356933 A026528 A150716 * A150717 A150718 A344558

Adjacent sequences: A151296 A151297 A151298 * A151300 A151301 A151302

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved