A149658 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, 0), (0, 0, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 59, 239, 995, 3967, 16685, 72029, 308013, 1326509, 5839973, 25751313, 113486965, 505253549, 2264923651, 10149497751, 45647471491, 206545814791, 936339133515, 4249377202291, 19357161132847, 88430112102083, 404359447342391, 1852486534010095, 8508801394789043, 39136469862569959

Offset

0,3

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, j, 1 + k, -1 + n] + aux[1 + i, 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: A090857 A287804 A149657 * A149659 A149660 A149661

Adjacent sequences: A149655 A149656 A149657 * A149659 A149660 A149661

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved