A149240 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, 1, 0), (0, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 36, 125, 451, 1627, 6114, 23313, 89669, 349271, 1377492, 5467197, 21844772, 87937757, 355984774, 1447373061, 5912845467, 24259828873, 99881034250, 412575338505, 1709751683474, 7105421773773, 29603546104182, 123641970713669, 517589863523413, 2171211944958415, 9125656546345446

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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A174993 A149238 A149239 * A149241 A149242 A149243

Adjacent sequences: A149237 A149238 A149239 * A149241 A149242 A149243

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved