A149938 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, 1, 0), (0, 1, 0), (1, 0, -1), (1, 0, 0)}.

1, 2, 5, 15, 49, 168, 608, 2300, 8924, 35440, 144058, 595413, 2493996, 10587961, 45467314, 197028767, 861179094, 3794348630, 16830451472, 75106043179, 337098044697, 1520780317049, 6892118979468, 31369336796327, 143347713844507, 657407221930884, 3025011229522799, 13963293967834988

Offset

0,2

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A301832 A272460 A149937 * A148365 A001892 A176025

Adjacent sequences: A149935 A149936 A149937 * A149939 A149940 A149941

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved