A150167 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, 0, 1), (0, 1, 0), (1, 0, -1), (1, 1, 0)}.

1, 2, 6, 20, 75, 297, 1221, 5172, 22380, 98629, 440778, 1993639, 9105180, 41934404, 194498667, 907672953, 4258455930, 20072573135, 95004367273, 451307179835, 2150894613835, 10281053786192, 49272219062531, 236702661167187, 1139581950206021, 5497253236717462, 26566243709140337, 128597831059720772

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A148482 A148483 A150166 * A150168 A145870 A134957

Adjacent sequences: A150164 A150165 A150166 * A150168 A150169 A150170

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved