A148941 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 9, 29, 101, 371, 1393, 5374, 21200, 84822, 344036, 1412127, 5848840, 24435170, 102820071, 435455990, 1854675147, 7939933182, 34146502646, 147461595987, 639215585208, 2780414939779, 12132310007732, 53093208374230, 232970574807063, 1024811888364982, 4518483009938097, 19965422326364515

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A162998 A275014 A278404 * A079319 A112532 A148942

Adjacent sequences: A148938 A148939 A148940 * A148942 A148943 A148944

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved