A149078 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), (1, -1, -1), (1, 1, 1)}.

1, 1, 4, 7, 28, 70, 244, 751, 2500, 8266, 28164, 92418, 327552, 1084792, 3864464, 13168347, 46660372, 162432234, 577642588, 2013423778, 7250734160, 25353048772, 91650888464, 323761950406, 1169400791664, 4170128595524, 15087888636240, 53874297465864, 196091859507472, 701527538468276, 2559230407751696

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[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: A149076 A123767 A149077 * A149079 A149080 A366314

Adjacent sequences: A149075 A149076 A149077 * A149079 A149080 A149081

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved