A150456 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, 1, 0), (1, 0, -1), (1, 1, 1)}.

1, 2, 7, 25, 95, 384, 1581, 6650, 28445, 122882, 536955, 2363807, 10478253, 46724020, 209360037, 942481707, 4259000203, 19313431126, 87856492233, 400762816537, 1832861493837, 8401749612752, 38595161969907, 177641636873186, 819090588693519, 3783092548698382, 17499656608020141, 81065468429816609

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 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: A150453 A150454 A150455 * A150457 A355628 A276903

Adjacent sequences: A150453 A150454 A150455 * A150457 A150458 A150459

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved