A149241 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), (-1, 1, 1), (0, -1, 0), (1, 1, 0)}.

1, 1, 4, 11, 36, 125, 453, 1615, 6132, 23315, 89109, 348805, 1375922, 5429329, 21765534, 87663419, 353523880, 1439753549, 5886395981, 24090905151, 99280297840, 410368064685, 1697958823134, 7060899122921, 29433783295882, 122811558530157, 514382368379719, 2158703728224241, 9067292750103322

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, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A149238 A149239 A149240 * A149242 A149243 A112849

Adjacent sequences: A149238 A149239 A149240 * A149242 A149243 A149244

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved