A149978 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), (-1, 1, 1), (0, 1, 0), (1, 0, -1), (1, 0, 0)}.

1, 2, 5, 16, 58, 221, 883, 3668, 15596, 67571, 298134, 1333912, 6030624, 27528761, 126746884, 587545554, 2739699560, 12845256385, 60510949814, 286203098987, 1358685159689, 6471768994331, 30917450082933, 148092751514563, 711095056485640, 3422022007694816, 16500729516301499, 79711807146475888

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, j, 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, -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: A184943 A286946 A184596 * A212263 A149979 A262441

Adjacent sequences: A149975 A149976 A149977 * A149979 A149980 A149981

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved