A150076 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), (0, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 18, 66, 237, 910, 3544, 14316, 57988, 240037, 1004974, 4250588, 18089218, 77781528, 336565989, 1463454865, 6397975200, 28130673287, 124136439392, 549725055665, 2444267057222, 10904730274771, 48773233678574, 218764249195940, 984016347295730, 4435970838967158, 20038228680358068

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 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: A052863 A037128 A150075 * A150077 A173385 A057693

Adjacent sequences: A150073 A150074 A150075 * A150077 A150078 A150079

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved