A150594 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, -1, 1), (0, 0, -1), (0, 1, 0), (1, 1, 1)}.

1, 2, 7, 27, 107, 438, 1845, 7908, 34303, 150348, 664775, 2960079, 13257289, 59674848, 269793959, 1224411921, 5575399047, 25463488884, 116605425929, 535256505307, 2462340230837, 11349906044252, 52410818984793, 242420589719182, 1123003680161339, 5209618624112916, 24199106376990991, 112543832348913445

Offset

0,2

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[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, 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: A136412 A360149 A192417 * A150595 A150596 A026726

Adjacent sequences: A150591 A150592 A150593 * A150595 A150596 A150597

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved