A150050 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), (0, 0, -1), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 2, 6, 18, 61, 216, 805, 3106, 12273, 49713, 204584, 856073, 3627081, 15541148, 67265699, 293557472, 1291371759, 5718657166, 25482111083, 114180541557, 514173146013, 2326225644455, 10568079142209, 48198378627602, 220604026242275, 1013030819655013, 4666248466740808, 21554720609186250

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[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: A150048 A363511 A150049 * A192318 A192483 A150051

Adjacent sequences: A150047 A150048 A150049 * A150051 A150052 A150053

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved