A151008 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, 0, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 38, 181, 843, 4094, 19725, 96741, 473095, 2333497, 11499024, 56921007, 281721629, 1397891341, 6937364429, 34480929307, 171425261244, 853082126951, 4246436420391, 21151337844682, 105380537001413, 525263331591173, 2618724523158942, 13059983607960857, 65144475949937196, 325025185736586747

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[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A105484 A151006 A151007 * A057647 A249925 A162972

Adjacent sequences: A151005 A151006 A151007 * A151009 A151010 A151011

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved