A149160 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, 1), (0, 1, -1), (0, 1, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 4, 9, 40, 113, 524, 1692, 8000, 27851, 133516, 489230, 2367023, 9001776, 43825044, 171427906, 838457474, 3352831063, 16457057856, 66986311271, 329704918985, 1361760481094, 6717282033726, 28085284883218, 138786178330022, 586330463687896, 2901667698657740, 12368725272527344, 61286020498105625

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, 1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A142239 A118639 A149159 * A149161 A149162 A149163

Adjacent sequences: A149157 A149158 A149159 * A149161 A149162 A149163

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved