A149403 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), (-1, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 52, 170, 792, 2958, 14057, 54619, 264029, 1068087, 5208579, 21555125, 105790375, 446084237, 2198685109, 9399635429, 46473502878, 200903485754, 995565199085, 4342682420690, 21556860426720, 94738071265023, 470894637973974, 2082599114595994, 10362169084078158, 46076752691587189

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A045906 A025282 A303392 * A127866 A149404 A149405

Adjacent sequences: A149400 A149401 A149402 * A149404 A149405 A149406

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved