A150851 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, 0, 0), (0, -1, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 8, 32, 140, 626, 2886, 13490, 63872, 305112, 1467868, 7102336, 34517496, 168387396, 823951534, 4042200638, 19873743788, 97891883374, 482955922222, 2385980736896, 11801790984722, 58436594936270, 289615703646050, 1436524045239548, 7130447748994688, 35415979831479054, 176007162177169918

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150849 A150850 A179469 * A150852 A150853 A150854

Adjacent sequences: A150848 A150849 A150850 * A150852 A150853 A150854

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved