A149865 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, 1, -1), (0, 0, 1), (0, 1, 0), (1, 0, -1)}.

1, 2, 5, 13, 40, 131, 452, 1572, 5692, 21031, 79417, 302186, 1169670, 4574232, 18083006, 71931274, 288765763, 1166819602, 4744411047, 19384558408, 79648672433, 328754264401, 1362556419965, 5668293251091, 23670909753372, 99178834662469, 416791226821262, 1756590772659012, 7424025056902146

Offset

0,2

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, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A291614 A202153 A149864 * A174146 A375677 A149866

Adjacent sequences: A149862 A149863 A149864 * A149866 A149867 A149868

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved