A149646 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, 0), (-1, 1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 71, 243, 1187, 4461, 22011, 86925, 430971, 1756329, 8734581, 36405705, 181377819, 768766449, 3834384729, 16464218723, 82179561905, 356541284253, 1780516964795, 7790655724523, 38918630095745, 171496944680321, 856925459181061, 3798786909959589, 18984750875779951, 84594695456424679

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149643 A149644 A149645 * A149647 A149648 A149649

Adjacent sequences: A149643 A149644 A149645 * A149647 A149648 A149649

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved