A150340 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, 1, 0)}.

1, 2, 7, 23, 88, 338, 1366, 5593, 23464, 99715, 429069, 1863567, 8165501, 36041316, 160061446, 714566337, 3205536363, 14441835139, 65311558665, 296338140683, 1348690796753, 6155350757000, 28164237220570, 129160967770829, 593577114799665, 2733219311301580, 12608404787147022, 58259585371373722

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150337 A150338 A150339 * A339038 A001338 A150341

Adjacent sequences: A150337 A150338 A150339 * A150341 A150342 A150343

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved