A149866 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), (0, 0, 1), (0, 1, 0), (1, -1, 0)}.

1, 2, 5, 13, 40, 134, 467, 1671, 6172, 23436, 90370, 354271, 1410448, 5681881, 23111260, 94915721, 393246863, 1640456796, 6888518741, 29110220069, 123682094892, 528032933464, 2264948231740, 9757427695261, 42194050729094, 183120618953859, 797497306584136, 3483922404178219, 15263691795321215

Offset

0,2

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, k, -1 + n] + aux[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: A149865 A174146 A375677 * A149867 A062704 A274909

Adjacent sequences: A149863 A149864 A149865 * A149867 A149868 A149869

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved