A149316 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), (1, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 11, 50, 184, 876, 3621, 17556, 76922, 376482, 1708220, 8409404, 39041608, 192940484, 910081407, 4509550244, 21515942178, 106817895330, 514014162986, 2555485893692, 12377644533456, 61603054201864, 299902792304566, 1493841562522540, 7302020406985320, 36395648984260868, 178487830419946360

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, -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: A149313 A149314 A149315 * A271426 A318120 A355337

Adjacent sequences: A149313 A149314 A149315 * A149317 A149318 A149319

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved