A148561 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, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 6, 18, 50, 153, 504, 1638, 5769, 20068, 72751, 266169, 988016, 3730735, 14171839, 54628042, 211739875, 828935479, 3265817469, 12950492111, 51683663416, 207238224437, 835593504655, 3382925340979, 13756348538770, 56151660690996, 230010511496891, 945408155934520, 3897506695343284

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A369530 A161006 A148560 * A123891 A148562 A148563

Adjacent sequences: A148558 A148559 A148560 * A148562 A148563 A148564

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved