A149159 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), (0, 0, -1), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 9, 40, 113, 524, 1692, 8000, 27819, 133388, 488738, 2363983, 8988630, 43753966, 171135009, 836912246, 3346439852, 16423513868, 66848509014, 328987390212, 1358794540968, 6701974649601, 28021600464895, 138459371554235, 584962744192593, 2894678009949290, 12339297165323228, 61136160909975661

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, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[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: A149158 A142239 A118639 * A149160 A149161 A149162

Adjacent sequences: A149156 A149157 A149158 * A149160 A149161 A149162

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved