A151080 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, 3, 10, 41, 168, 727, 3219, 14413, 65753, 301757, 1398665, 6523081, 30582968, 144132159, 681785699, 3237085331, 15416598377, 73621489721, 352454733824, 1691006510764, 8129254763605, 39151020033494, 188860503597557, 912424715585327, 4414179532977892, 21382355779573120, 103698957821381670

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[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: A149058 A151078 A151079 * A153474 A151081 A152802

Adjacent sequences: A151077 A151078 A151079 * A151081 A151082 A151083

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved