A148273 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, -1, 1), (-1, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 4, 15, 40, 143, 416, 1713, 5656, 22700, 76363, 329653, 1187031, 5016800, 18190009, 80531373, 305215724, 1328055225, 5041718093, 22685251909, 88921805740, 394197025928, 1544017602555, 7025574349024, 28206914186360, 126676719647114, 507576081896187, 2328626270429861

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A148270 A148271 A148272 * A148274 A148275 A148276

Adjacent sequences: A148270 A148271 A148272 * A148274 A148275 A148276

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved