A149770 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, 0, 0), (-1, 1, 1), (0, -1, 1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 75, 315, 1343, 5805, 25469, 112617, 501885, 2250049, 10139301, 45886365, 208442445, 949943279, 4341663243, 19894045759, 91366143203, 420480670439, 1938759043735, 8954642063739, 41424603644035, 191911504267863, 890285766867387, 4135254546142935, 19230149489020755, 89523642639196751

Offset

0,3

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, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149767 A149768 A149769 * A285424 A275859 A323269

Adjacent sequences: A149767 A149768 A149769 * A149771 A149772 A149773

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved