A149320 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, 0), (0, 0, -1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 37, 139, 528, 1941, 7746, 31595, 127242, 525422, 2225527, 9398419, 39954756, 172778903, 750568243, 3264066086, 14327170089, 63317552889, 280166179079, 1244896632989, 5564896945438, 24937018367491, 111969319687122, 504816947007271, 2282959607165593, 10340149412130944

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[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A280891 A362886 A149319 * A362146 A149321 A149322

Adjacent sequences: A149317 A149318 A149319 * A149321 A149322 A149323

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved