A148362 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, 0, 1), (-1, 1, 1), (0, 0, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 15, 46, 162, 573, 2186, 8411, 33783, 136964, 570345, 2395284, 10241316, 44112212, 192417802, 844668469, 3742462954, 16672149834, 74799056643, 337155007308, 1528184417633, 6954558011029, 31791403631798, 145834990404475, 671458714209519, 3100927196427213, 14365248430386121

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, j, 1 + k, -1 + n] + aux[-1 + 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, 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: A148360 A148361 A346521 * A143094 A308274 A058495

Adjacent sequences: A148359 A148360 A148361 * A148363 A148364 A148365

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved