A151139 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, 1), (0, 1, -1), (0, 1, 0), (0, 1, 1), (1, 0, 1)}

1, 3, 11, 46, 204, 915, 4218, 19712, 92635, 439500, 2097879, 10045349, 48320283, 233190823, 1127688064, 5467521609, 26562531710, 129235130543, 629811090988, 3073516948545, 15015174203835, 73438632955616, 359542851326497, 1761726779178020, 8639634327302590, 42401462680673052, 208234844528758384

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A151136 A151137 A151138 * A301412 A198413 A151140

Adjacent sequences: A151136 A151137 A151138 * A151140 A151141 A151142

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved