A149111 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, 0, 0), (-1, 1, 1), (1, -1, -1), (1, 1, 0)}.

1, 1, 4, 8, 36, 100, 458, 1462, 6809, 23521, 111180, 405288, 1935161, 7330542, 35252989, 137422833, 664576216, 2649175259, 12867856516, 52224563411, 254550418677, 1048465569279, 5124668686800, 21370196670463, 104693461764880, 441179953011886, 2165508882775008, 9208165544591383, 45270898259206533

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A269012 A149110 A354735 * A149112 A221842 A100214

Adjacent sequences: A149108 A149109 A149110 * A149112 A149113 A149114

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved