A148399 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, 1), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 16, 54, 192, 720, 2703, 10516, 41705, 168001, 689349, 2859808, 12006070, 50816519, 217011153, 932736893, 4035832654, 17565418331, 76834165053, 337790073171, 1491128371657, 6609622369168, 29400175070022, 131221249915403, 587446331571253, 2637383430625903, 11872227572864716

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, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A149962 A149963 A149964 * A149965 A149966 A149967

Adjacent sequences: A148396 A148397 A148398 * A148400 A148401 A148402

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved