A149097 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), (-1, 0, 0), (-1, 1, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 8, 33, 85, 369, 1079, 4811, 15263, 69320, 232480, 1069395, 3735813, 17351692, 62541448, 292641635, 1081249221, 5089473600, 19187812058, 90753730279, 347934682697, 1652262396851, 6424923779881, 30613860682437, 120499305565195, 575826681275548, 2290541991358632, 10973200218688887

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A173652 A149095 A149096 * A149098 A149099 A149100

Adjacent sequences: A149094 A149095 A149096 * A149098 A149099 A149100

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved