A149228 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, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 10, 46, 146, 696, 2472, 12001, 45483, 223022, 881542, 4348583, 17699412, 87646682, 364484570, 1809577040, 7649804945, 38047511026, 162936769267, 811426736660, 3511428349970, 17503203877425, 76400925952003, 381093314584880, 1675546177429929, 8362071716152935, 36992673643317585

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A153985 A184481 A149227 * A149229 A149230 A115327

Adjacent sequences: A149225 A149226 A149227 * A149229 A149230 A149231

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved