A149329 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), (-1, 1, 0), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 39, 148, 550, 2071, 8161, 32396, 128707, 521583, 2129664, 8706306, 35920334, 149087733, 619863981, 2589541208, 10865234502, 45674123835, 192548458938, 814243566145, 3449403678162, 14641287502016, 62285013815016, 265384423471876, 1132421803033238, 4840177356527085

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A122920 A241073 A149328 * A149330 A149331 A009532

Adjacent sequences: A149326 A149327 A149328 * A149330 A149331 A149332

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved