A151321 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), (0, 1), (1, -1), (1, 0), (1, 1)}.

1, 3, 13, 59, 279, 1341, 6527, 31995, 157659, 779601, 3864985, 19197119, 95485691, 475450235, 2369357063, 11815028649, 58946549799, 294208885315, 1468899193277, 7335669719437, 36641882024645, 183058171254391, 914661462596977, 4570679817175993, 22842398781064325, 114165818614661101

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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

Crossrefs

Sequence in context: A151230 A151231 A299502 * A151232 A151233 A151234

Adjacent sequences: A151318 A151319 A151320 * A151322 A151323 A151324

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved