A148096 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, -1, 1), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 10, 25, 76, 231, 743, 2389, 7896, 26880, 93731, 332056, 1186315, 4276398, 15613592, 57674835, 215106287, 807023678, 3045302991, 11566813790, 44234290091, 170156563119, 657452881298, 2550494701625, 9935922370990, 38875057057452, 152697762641138, 601752794728566, 2378478902181928

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A148094 A148095 A124419 * A006901 A123422 A123413

Adjacent sequences: A148093 A148094 A148095 * A148097 A148098 A148099

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved