A149891 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), (0, 0, 1), (0, 1, 1), (1, -1, 0)}.

1, 2, 5, 14, 45, 153, 548, 2019, 7617, 29412, 115631, 460957, 1862485, 7607179, 31357468, 130386179, 546204674, 2303103834, 9770915090, 41679263631, 178659773792, 769340135930, 3326719798655, 14439860987742, 62900346313029, 274897072613460, 1205054156763758, 5297624732877279

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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + 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: A149888 A149889 A149890 * A149892 A149893 A149894

Adjacent sequences: A149888 A149889 A149890 * A149892 A149893 A149894

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved