A148596 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, 0), (0, 0, -1), (0, 1, 1), (1, -1, -1)}.

1, 1, 3, 6, 20, 58, 181, 614, 2019, 7141, 25123, 89366, 329988, 1206024, 4505670, 17008519, 64177639, 246706347, 948075463, 3668414666, 14342199627, 56019992182, 220812556828, 873603491381, 3462242838291, 13825132525614, 55246790176433, 221663473337181, 893383939279763, 3602947976899024

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148594 A148595 A214821 * A148597 A148598 A148599

Adjacent sequences: A148593 A148594 A148595 * A148597 A148598 A148599

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved