A149363 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, 0, 0), (1, -1, 0), (1, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 44, 160, 635, 2520, 10374, 43134, 183372, 785862, 3413850, 14943786, 66054417, 293780916, 1315917746, 5925586810, 26832235430, 122037157814, 557522216602, 2556606994682, 11767063971676, 54332854794374, 251652806269006, 1168810615051590, 5442994681797090, 25408401050126850

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A149360 A149361 A149362 * A188632 A151460 A149364

Adjacent sequences: A149360 A149361 A149362 * A149364 A149365 A149366

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved