A150435 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, 0), (1, 1, 0)}.

1, 2, 7, 24, 99, 403, 1754, 7685, 34615, 157138, 724092, 3359140, 15717016, 73961981, 349987423, 1663258901, 7936993440, 37999635136, 182481367565, 878650252569, 4240640613099, 20509555802674, 99383747822983, 482402000559299, 2345172245872755, 11417146504183784, 55653887338699863, 271608882010579778

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 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: A325581 A162044 A150434 * A150436 A197553 A213950

Adjacent sequences: A150432 A150433 A150434 * A150436 A150437 A150438

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved