A150107 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, 1, 0), (0, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 19, 69, 258, 1014, 4082, 16800, 70383, 299011, 1284372, 5572651, 24374059, 107358625, 475819313, 2120059036, 9490995387, 42668497139, 192542510134, 871799541820, 3959436307454, 18032344193044, 82332352883961, 376785054885822, 1727985033292291, 7940321135142378, 36553005597894890

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, -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: A058122 A150105 A150106 * A148472 A150108 A150109

Adjacent sequences: A150104 A150105 A150106 * A150108 A150109 A150110

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved