A149982 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, 0), (-1, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 55, 200, 737, 2772, 10763, 41806, 166215, 662867, 2674845, 10868017, 44389916, 182614079, 753678185, 3127891664, 13020561792, 54411159168, 228060902666, 958555573998, 4039944233710, 17064192758861, 72245743738260, 306447994365643, 1302407521525901, 5544514997391690

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[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A148409 A149980 A149981 * A149983 A149984 A149985

Adjacent sequences: A149979 A149980 A149981 * A149983 A149984 A149985

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved