A149115 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, 1), (-1, 0, 0), (0, -1, 0), (1, 1, 0)}.

1, 1, 4, 9, 32, 95, 335, 1143, 4040, 14731, 53837, 200909, 755416, 2877693, 11045026, 42621291, 166279678, 650781327, 2562641223, 10144316095, 40347911762, 161069462279, 645317015486, 2596732415493, 10476529973522, 42390528499901, 172069218391077, 700239842575225, 2855891190676346

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, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A322780 A343547 A151271 * A149116 A149117 A149118

Adjacent sequences: A149112 A149113 A149114 * A149116 A149117 A149118

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved