A150022 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, -1, 0), (1, 0, 0)}.

1, 2, 5, 18, 67, 258, 1054, 4336, 18390, 79546, 346789, 1536833, 6851192, 30817749, 139841923, 637266870, 2924137611, 13471986079, 62332135243, 289725945703, 1350473477529, 6318046817743, 29638426526944, 139393817258063, 657399735735674, 3106530600891371, 14713492006420404, 69818773620573288

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, j, k, -1 + n] + aux[-1 + i, 1 + 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: A150020 A144721 A150021 * A150023 A150024 A150025

Adjacent sequences: A150019 A150020 A150021 * A150023 A150024 A150025

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved