A149598 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, 0, -1), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 15, 59, 225, 933, 3823, 16233, 69369, 301099, 1315451, 5802899, 25746201, 114961725, 515787391, 2324699601, 10518350007, 47762776009, 217552606081, 993787275321, 4551341305097, 20892882712281, 96115052753577, 443040439980111, 2045857584859099, 9463210149521435, 43840590037201127

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 1 + k, -1 + n] + aux[i, 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: A149595 A149596 A149597 * A149599 A149600 A369555

Adjacent sequences: A149595 A149596 A149597 * A149599 A149600 A149601

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved