A148095 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, 1), (-1, 0, 0), (0, 0, 1), (0, 1, -1), (1, -1, 0)}.

1, 1, 2, 4, 10, 25, 75, 222, 696, 2203, 7371, 24787, 86008, 301117, 1077079, 3884641, 14241326, 52666805, 196980204, 742074660, 2821601164, 10806383704, 41688390675, 161765527299, 631511352222, 2479059137090, 9782815644799, 38784291290400, 154442952504946, 617627277390419, 2479845218105827

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 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, -1 + 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: A148093 A206289 A148094 * A124419 A148096 A006901

Adjacent sequences: A148092 A148093 A148094 * A148096 A148097 A148098

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved