A148351 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, 0), (0, -1, 1), (0, 0, 1), (0, 1, -1), (1, -1, 1)}.

1, 1, 2, 5, 15, 44, 147, 495, 1758, 6392, 23877, 90960, 352682, 1388471, 5536070, 22333566, 90999168, 374144507, 1550788644, 6474314495, 27208663317, 115026686024, 488951418197, 2088810690352, 8964559511261, 38636855716466, 167177656758582, 726003687715148, 3163527887839747

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A071742 A035355 A220873 * A148352 A151463 A148353

Adjacent sequences: A148348 A148349 A148350 * A148352 A148353 A148354

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved