A149603 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, 0, 0), (1, -1, -1), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 61, 227, 973, 3937, 17167, 72373, 321081, 1391267, 6240225, 27514269, 124476035, 556062373, 2532538727, 11423137407, 52302372255, 237698999627, 1093135607439, 4998032956757, 23069307578603, 105995590304017, 490770438931079, 2264137425006343, 10511419103819741, 48660380681391729

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, 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: A207969 A149601 A149602 * A149604 A149605 A149606

Adjacent sequences: A149600 A149601 A149602 * A149604 A149605 A149606

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved