A148113 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 10, 29, 85, 272, 881, 2994, 10457, 37331, 136186, 504933, 1900834, 7262202, 28045612, 109579558, 432061289, 1718479515, 6892069642, 27827372942, 113161355347, 462806743799, 1903851701162, 7872444929653, 32707528220258, 136523024560819, 572157561922896, 2407617702772050

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 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, 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: A148111 A148112 A224845 * A243814 A005505 A262592

Adjacent sequences: A148110 A148111 A148112 * A148114 A148115 A148116

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved