A148316 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, 0)}.

1, 1, 2, 5, 14, 39, 124, 400, 1358, 4680, 16821, 60975, 227420, 854978, 3284367, 12695918, 49903145, 197196052, 789692499, 3176716632, 12918607435, 52741268340, 217271153314, 898126282267, 3740877574014, 15628602402197, 65718067398013, 277087115116637, 1174844573892291, 4993340224586904

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[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: A003054 A317553 A370723 * A148317 A148318 A148319

Adjacent sequences: A148313 A148314 A148315 * A148317 A148318 A148319

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved