A151242 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), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 4, 16, 66, 288, 1298, 5928, 27390, 128082, 603852, 2862322, 13638202, 65286884, 313627614, 1510990514, 7299643480, 35348690964, 171512134246, 833651714848, 4058675334414, 19788039958888, 96597812714834, 472104261808508, 2309782727305422, 11311443788064134, 55442671975666152, 271971493598145002

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A110276 A026883 A349730 * A218645 A273582 A183275

Adjacent sequences: A151239 A151240 A151241 * A151243 A151244 A151245

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved