A149161 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), (-1, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 9, 40, 114, 528, 1703, 8060, 28046, 134504, 492714, 2383928, 9063508, 44127320, 172559091, 844018252, 3374183038, 16561875136, 67397982670, 331727733384, 1369846371868, 6757092675160, 28246826894110, 139582693099384, 589605775705292, 2917837189521072, 12435985878882788, 61618484473063792

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[-1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A118639 A149159 A149160 * A149162 A149163 A149164

Adjacent sequences: A149158 A149159 A149160 * A149162 A149163 A149164

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved