A148908 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, 1), (0, -1, 1), (0, 1, 1), (1, 1, -1)}.

1, 1, 3, 8, 32, 106, 427, 1596, 6692, 26473, 113271, 466467, 2030691, 8571835, 37813319, 162709710, 725083181, 3163603626, 14215151860, 62732129567, 283740210409, 1263357748284, 5745970779015, 25778095765935, 117783653397422, 531685829933668, 2438998668578503, 11069078488724286, 50949585815926378

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, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148905 A148906 A148907 * A148909 A148910 A148911

Adjacent sequences: A148905 A148906 A148907 * A148909 A148910 A148911

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved