A149247 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, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 4, 11, 38, 116, 440, 1453, 5530, 18794, 72792, 257238, 992644, 3549594, 13853496, 50447453, 196718714, 721500978, 2829371848, 10503154516, 41147601932, 153417689174, 603530012488, 2267966093122, 8917294536916, 33615803655530, 132535696401192, 502544406495538, 1980452388616776

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A130494 A027573 A149246 * A149248 A149249 A149250

Adjacent sequences: A149244 A149245 A149246 * A149248 A149249 A149250

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved