A150546 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, 0), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 26, 104, 429, 1803, 7782, 33856, 148730, 660726, 2948863, 13237899, 59758894, 270693518, 1230751350, 5614377090, 25678567655, 117745736266, 541132227323, 2491918243663, 11496651079775, 53130402214928, 245919723193033, 1139897903189075, 5290724990386423, 24586936743438214, 114391228364278238

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A150544 A345884 A150545 * A151296 A141370 A150547

Adjacent sequences: A150543 A150544 A150545 * A150547 A150548 A150549

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved