A149533 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, -1), (-1, -1, 0), (0, 1, -1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 49, 177, 645, 2521, 9653, 38409, 152453, 616017, 2495933, 10203805, 41971201, 173082373, 719670741, 2991784285, 12531776661, 52482689565, 221024161045, 931529633897, 3939885956705, 16692931806241, 70862610871997, 301532473203261, 1284316853391157, 5483956190912425

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A343549 A084601 A149532 * A149534 A149535 A149536

Adjacent sequences: A149530 A149531 A149532 * A149534 A149535 A149536

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved