A149367 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, 0), (-1, 1, 1), (0, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 45, 160, 678, 2689, 10987, 46623, 200648, 853429, 3708622, 16347640, 71949049, 317419539, 1419224447, 6362428004, 28500854794, 128527458182, 582669917201, 2641128719409, 12001433948192, 54787460741349, 250485402351848, 1146059928297438, 5259296181310155, 24189261693161814

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, 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, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A074035 A149366 A370540 * A149368 A200539 A149369

Adjacent sequences: A149364 A149365 A149366 * A149368 A149369 A149370

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved