A149330 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, 0), (-1, 0, 0), (-1, 1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 39, 148, 550, 2073, 8163, 32415, 128870, 521964, 2131786, 8718262, 35959256, 149267043, 620741014, 2592823626, 10879365183, 45738855833, 192807224404, 815333606093, 3454225929696, 14661217666256, 62368650443349, 265747561015488, 1133948758531347, 4846603982947246

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A241073 A149328 A149329 * A149331 A009532 A248325

Adjacent sequences: A149327 A149328 A149329 * A149331 A149332 A149333

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved