A149621 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, -1, 1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 65, 247, 1073, 4429, 19531, 83855, 374813, 1646373, 7436141, 33160711, 150961707, 680557859, 3116996709, 14167970351, 65200939457, 298276795781, 1378001669359, 6336574350495, 29368668897235, 135618551033187, 630280983790681, 2920720543034943, 13605821062219949, 63235825225518767

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + 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: A323793 A149619 A149620 * A149622 A247281 A149623

Adjacent sequences: A149618 A149619 A149620 * A149622 A149623 A149624

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved