A148361 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), (-1, 1, 1), (0, 0, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 2, 5, 15, 46, 160, 567, 2130, 8196, 32488, 131481, 541914, 2269092, 9626174, 41318215, 179138680, 783632812, 3455177987, 15342105002, 68557162752, 308103758161, 1391838174807, 6317203472894, 28795740786596, 131778561936655, 605252272507475, 2789217930709190, 12893601640890090

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + 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: A360272 A268648 A148360 * A346521 A148362 A143094

Adjacent sequences: A148358 A148359 A148360 * A148362 A148363 A148364

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved