A150580 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, 1), (0, 1, -1), (1, -1, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 26, 109, 473, 2129, 9781, 45693, 215988, 1030642, 4953855, 23950353, 116341574, 567338652, 2775523875, 13614961348, 66938282042, 329739787878, 1626995769346, 8039338732382, 39773168578761, 196982080297641, 976498313349242, 4844789335263682, 24054403887999265, 119507267843844061

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150578 A150579 A093638 * A150581 A150582 A150583

Adjacent sequences: A150577 A150578 A150579 * A150581 A150582 A150583

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved