A148404 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, 0, 1), (0, 0, 1), (1, -1, -1), (1, 1, -1)}.

1, 1, 2, 5, 17, 50, 183, 612, 2427, 8825, 36059, 138389, 581717, 2316687, 9922307, 40628935, 176649853, 738938555, 3250269764, 13829300753, 61402897922, 264875758505, 1185178057988, 5170848320772, 23286936959696, 102567165143373, 464457815281869, 2062198363246999, 9382546018637717

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + 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: A148401 A148402 A148403 * A061675 A148405 A216969

Adjacent sequences: A148401 A148402 A148403 * A148405 A148406 A148407

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved