A148353 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, 0, 1), (1, 0, -1), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 5, 15, 44, 154, 514, 1949, 7100, 28289, 109269, 450989, 1814897, 7692208, 31909424, 138042852, 586240058, 2577374384, 11152156893, 49670880217, 218216089703, 982348019505, 4370272299508, 19850169852979, 89244498210728, 408439137023100, 1852782584365454, 8534857228606366

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, 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: A148351 A148352 A151463 * A336417 A232208 A294502

Adjacent sequences: A148350 A148351 A148352 * A148354 A148355 A148356

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved