A150514 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, 1), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 25, 103, 423, 1867, 8180, 37395, 169782, 792576, 3678418, 17406501, 81974128, 391563653, 1863052796, 8959881496, 42952712261, 207628630330, 1001034036543, 4858094782656, 23526234731024, 114534690896589, 556616229657639, 2716755245396593, 13240761730504033, 64762702027490147

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, 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: A097597 A150512 A150513 * A150515 A150516 A150517

Adjacent sequences: A150511 A150512 A150513 * A150515 A150516 A150517

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved