A150008 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, 1, 0), (1, -1, -1), (1, 0, 1)}.

1, 2, 5, 17, 60, 226, 878, 3464, 14021, 57807, 241666, 1023174, 4367445, 18782294, 81402927, 355139477, 1558645747, 6875471321, 30454291424, 135423012261, 604468388810, 2707499454308, 12166075615983, 54821229666088, 247644267892085, 1121332891514782, 5088935535980582, 23144721507136603

Offset

0,2

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, 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, 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: A150005 A150006 A150007 * A150009 A150010 A150011

Adjacent sequences: A150005 A150006 A150007 * A150009 A150010 A150011

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved