A150173 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, 0), (0, 0, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 6, 20, 77, 288, 1154, 4629, 19430, 80553, 344561, 1466736, 6394069, 27657644, 121879990, 534480899, 2379888298, 10536644015, 47245113964, 210938882127, 952083417273, 4278003642079, 19403565251164, 87684756958164, 399536723692068, 1813772487405633, 8294461398981496, 37810209148921878

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A000898 A213225 A195254 * A150174 A150175 A150176

Adjacent sequences: A150170 A150171 A150172 * A150174 A150175 A150176

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved