A150483 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), (0, 0, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 25, 100, 409, 1696, 7230, 31218, 136348, 601392, 2668866, 11926440, 53590116, 241861429, 1096236518, 4985474479, 22743466843, 104053210697, 477225366201, 2193758211686, 10105182346741, 46633811335305, 215580754238987, 998167033562149, 4628378289705604, 21490258193373055, 99906737241167235

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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: A150480 A150481 A150482 * A150484 A150485 A150486

Adjacent sequences: A150480 A150481 A150482 * A150484 A150485 A150486

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved