A149007 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, 0, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 34, 120, 483, 1886, 7877, 32410, 139157, 590465, 2582112, 11196190, 49611062, 218515018, 978137394, 4358768473, 19667296795, 88439181398, 401608599218, 1819068892941, 8304078080515, 37835168368298, 173480557890280, 794279796478468, 3655550464599447, 16805784722604018

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149004 A149005 A149006 * A053791 A296223 A045627

Adjacent sequences: A149004 A149005 A149006 * A149008 A149009 A149010

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved