A150085 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, -1, 1), (0, 1, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 6, 19, 65, 241, 905, 3599, 14425, 59534, 249329, 1056921, 4552398, 19735824, 86589754, 382354053, 1700890992, 7617683252, 34282253718, 155195308290, 705421980080, 3220837523649, 14762428021071, 67892389467223, 313323316552737, 1450092203641912, 6730788726949523, 31321971802780059

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[-1 + i, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A212380 A150084 A275755 * A306175 A266466 A005654

Adjacent sequences: A150082 A150083 A150084 * A150086 A150087 A150088

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved