A150504 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, 1, 1), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 25, 102, 413, 1733, 7380, 31942, 139818, 616646, 2741188, 12256906, 55097109, 248807269, 1127810540, 5130534695, 23408654831, 107101683780, 491227236154, 2258026100392, 10400718008600, 47994423938509, 221850329164811, 1027081986270860, 4761862152249699, 22107074616178501, 102760016462579821

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, -1 + 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: A150501 A150502 A150503 * A150505 A150506 A150507

Adjacent sequences: A150501 A150502 A150503 * A150505 A150506 A150507

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved