A149568 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, 1), (-1, 1, 1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 61, 201, 961, 3485, 16953, 65057, 318501, 1270385, 6239385, 25567503, 125918427, 526336207, 2597780455, 11027051415, 54512432667, 234248644823, 1159487821623, 5032467482813, 24935946686145, 109128642457511, 541205201186051, 2385127987378705, 11837318239533357, 52480754874395537

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[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A051859 A151275 A149567 * A201805 A144725 A051902

Adjacent sequences: A149565 A149566 A149567 * A149569 A149570 A149571

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved