A151259 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, 1, 2, 5, 13, 35, 104, 309, 950, 3001, 9580, 31122, 102447, 340154, 1141687, 3861440, 13151163, 45099030, 155500732, 538992037, 1877191730, 6565129272, 23052066243, 81232416035, 287194928135, 1018509372930, 3622229673983, 12916151094960, 46169898399992, 165415989450629, 593924178778286, 2136775816554616

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[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: A339294 A272064 A000747 * A149853 A148291 A148292

Adjacent sequences: A151256 A151257 A151258 * A151260 A151261 A151262

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved