A149117 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, 0, 0), (-1, 1, -1), (0, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 32, 101, 347, 1243, 4498, 16617, 63167, 240235, 931568, 3647803, 14370312, 57180711, 229115778, 922313297, 3737973883, 15221602137, 62225061536, 255556165925, 1053396408250, 4355324548631, 18069755065816, 75182656479519, 313582517369107, 1311433840151317, 5497064374143140

Offset

0,3

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, -1 + j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A151271 A149115 A149116 * A149118 A149119 A149120

Adjacent sequences: A149114 A149115 A149116 * A149118 A149119 A149120

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved