A149508 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, 0), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 11, 47, 155, 567, 2221, 8317, 32641, 130645, 512301, 2088841, 8448001, 34267705, 141725419, 581403191, 2405519927, 10036856947, 41688954635, 174672387397, 733626444877, 3078425686119, 13004805741757, 54936330467611, 232367878907401, 987307341570045, 4192369045556859

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 1 + j, 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: A149505 A149506 A149507 * A149509 A149510 A149511

Adjacent sequences: A149505 A149506 A149507 * A149509 A149510 A149511

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved