A151137 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), (0, 1, -1), (0, 1, 1), (1, 0, 0), (1, 1, 0)}

1, 3, 11, 46, 202, 918, 4272, 20146, 96096, 462150, 2236092, 10874695, 53093518, 260052412, 1277167839, 6286177214, 30998213081, 153099530722, 757172956854, 3749059996968, 18581735924770, 92178653535345, 457622970937958, 2273410063927890, 11300723380227944, 56203564918917070, 279656667570882248

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A151135 A307816 A151136 * A151138 A151139 A301412

Adjacent sequences: A151134 A151135 A151136 * A151138 A151139 A151140

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved