A149178 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, 0, -1), (-1, 0, 1), (0, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 35, 124, 432, 1653, 6238, 24009, 95031, 374816, 1502701, 6081138, 24653680, 101007864, 415326581, 1714309061, 7118874021, 29629533128, 123789902876, 518981830701, 2180354287790, 9187801076310, 38803381924060, 164201253368975, 696395326261535, 2958461375328120, 12589876811836979

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A149176 A059710 A149177 * A344559 A318701 A152916

Adjacent sequences: A149175 A149176 A149177 * A149179 A149180 A149181

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved