A149800 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), (1, -1, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 87, 363, 1735, 7717, 37377, 172405, 842961, 3969177, 19518485, 93212797, 460143557, 2218880423, 10983882619, 53341437199, 264580362679, 1291708896727, 6416774513695, 31454760994923, 156438640458835, 769300039796771, 3829561705630703, 18879985489563915, 94052258269651535

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, 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: A149797 A149798 A149799 * A147099 A323788 A351373

Adjacent sequences: A149797 A149798 A149799 * A149801 A149802 A149803

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved