A148827 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), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 27, 85, 309, 1081, 4049, 14846, 57700, 220417, 868886, 3391316, 13641655, 54422537, 221000582, 892890628, 3671515220, 15034249963, 62252763685, 257099572289, 1073686090460, 4474451273263, 18786656060621, 78779380559729, 332824779239776, 1404731718280666, 5960097991188767

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, 1 + k, -1 + n] + aux[-1 + i, 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: A148824 A148825 A148826 * A148828 A148829 A148830

Adjacent sequences: A148824 A148825 A148826 * A148828 A148829 A148830

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved