A150267 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, 0), (1, 0, -1), (1, 0, 1)}.

1, 2, 6, 22, 89, 370, 1585, 6986, 31317, 142230, 654000, 3035518, 14185121, 66714076, 315565582, 1499290539, 7150770043, 34228613264, 164347352327, 791165781965, 3817852791465, 18463872731698, 89464611676312, 434234627305046, 2111009783379968, 10277298441170561, 50098781177467074, 244508877664193913

Offset

0,2

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A150265 A150266 A165522 * A271388 A165540 A363809

Adjacent sequences: A150264 A150265 A150266 * A150268 A150269 A150270

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved