A149768 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, 0), (0, -1, 1), (1, -1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 75, 309, 1309, 5649, 24721, 109013, 484499, 2167671, 9753219, 44086523, 200053085, 910890547, 4160129705, 19051066455, 87452693175, 402311127209, 1854387999425, 8562773937655, 39603891522993, 183447996794325, 850922033479563, 3952070054383625, 18377175315765777, 85549466616749623

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[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A126392 A206373 A149767 * A149769 A149770 A285424

Adjacent sequences: A149765 A149766 A149767 * A149769 A149770 A149771

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved