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A151324 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, -1), (1, 0), (1, 1)} 0
1, 3, 14, 68, 351, 1863, 10097, 55554, 309103, 1735153, 9809244, 55775457, 318669544, 1828103920, 10523723262, 60763155726, 351760568907, 2041044528590, 11867027645777, 69122488251435, 403276604574906, 2356259190114886, 13785394936424951, 80749380782254502, 473518966715273252 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..24.

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[-1 + 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: A181662 A241478 A113140 * A121185 A276904 A199314

Adjacent sequences:  A151321 A151322 A151323 * A151325 A151326 A151327

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified April 12 18:58 EDT 2021. Contains 342932 sequences. (Running on oeis4.)