A149434 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 1, 1)}.

1, 1, 4, 13, 46, 164, 606, 2239, 8472, 31920, 122158, 466494, 1797288, 6923488, 26811944, 103876331, 403901878, 1571264580, 6128614886, 23917209854, 93517065586, 365867191042, 1433433089074, 5619276707450, 22052884573432, 86593169212632, 340319969605758, 1338154414920772, 5265502775297050

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149433 A047154 A180144 * A026641 A149435 A149436

Adjacent sequences: A149431 A149432 A149433 * A149435 A149436 A149437

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved