A151226 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), (0, 1, -1), (1, 0, 1), (1, 1, 0), (1, 1, 1)}.

1, 3, 13, 58, 268, 1274, 6103, 29578, 144191, 706114, 3471529, 17111174, 84533573, 418347563, 2073295781, 10287239649, 51092700553, 253964860179, 1263247273324, 6287222042418, 31307431744880, 155964283770448, 777259889839215, 3874804737467137, 19322276999093931, 96377663750354783

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[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: A326984 A296771 A270786 * A151320 A151227 A151228

Adjacent sequences: A151223 A151224 A151225 * A151227 A151228 A151229

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved