A150833 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, 0), (0, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 8, 32, 136, 594, 2674, 12192, 56252, 262166, 1231614, 5819164, 27637200, 131855458, 631385426, 3032777480, 14608882116, 70545450862, 341384364454, 1655193837812, 8039154612280, 39105952390138, 190492183707386, 929104570882912, 4536876256793644, 22177212994099974, 108512065189640142

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, -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, 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: A084607 A006139 A150832 * A198760 A150834 A150835

Adjacent sequences: A150830 A150831 A150832 * A150834 A150835 A150836

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved