A149106 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, 0, 1), (1, -1, -1), (1, 1, 0)}.

1, 1, 4, 8, 34, 91, 386, 1205, 5146, 17422, 75144, 267296, 1161554, 4276938, 18677450, 70571075, 309208856, 1191846297, 5234648979, 20497505744, 90190143442, 357689841471, 1576087185005, 6316705181733, 27864624569679, 112664602409092, 497446084425379, 2026418825472279, 8953939800573176

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 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: A200159 A149104 A149105 * A149107 A197157 A324410

Adjacent sequences: A149103 A149104 A149105 * A149107 A149108 A149109

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved