A151129 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, 1), (0, 0, 1), (1, 0, 1), (1, 1, 0)}

1, 3, 11, 45, 197, 872, 3983, 18439, 86108, 405885, 1926008, 9180468, 43971432, 211334511, 1018756854, 4924594051, 23857317607, 115808367636, 563173460823, 2742840860644, 13377406360982, 65326918131829, 319371224969523, 1562969595017468, 7656182764050154, 37535645510369349, 184170600862110913

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A049155 A063024 A217887 * A151130 A216949 A074532

Adjacent sequences: A151126 A151127 A151128 * A151130 A151131 A151132

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved