A148317 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, 1), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 14, 39, 125, 393, 1338, 4568, 16140, 57955, 211441, 784037, 2938223, 11144377, 42656950, 164683455, 640849659, 2510334400, 9898182076, 39244156602, 156425354900, 626478426609, 2520086142119, 10179070688974, 41269184569820, 167910469044899, 685397571233314, 2806297972718526

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, 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] + 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: A003054 A317553 A148316 * A148318 A148319 A126219

Adjacent sequences: A148314 A148315 A148316 * A148318 A148319 A148320

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved