A150844 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, 1, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 8, 32, 138, 616, 2820, 13135, 61942, 294979, 1415255, 6831215, 33132451, 161335664, 788202460, 3861396249, 18961249047, 93294506192, 459822319237, 2269699564120, 11217792789310, 55505598311770, 274914136943199, 1362817202781076, 6761063939889804, 33565419170916940, 166738698603993248

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + 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: A274483 A308152 A150843 * A141380 A151304 A151828

Adjacent sequences: A150841 A150842 A150843 * A150845 A150846 A150847

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved