A148390 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, 0, 1), (0, 0, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 16, 52, 165, 560, 2005, 7345, 27309, 102070, 389673, 1511857, 5920738, 23410137, 92986782, 372761982, 1506441428, 6122389601, 25027007251, 102632553459, 423107823161, 1752962129286, 7289525096624, 30427717831459, 127313391094280, 534546700397736, 2251892781541432

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[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A303477 A234843 A011819 * A232317 A148391 A337268

Adjacent sequences: A148387 A148388 A148389 * A148391 A148392 A148393

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved