A149236 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, 0), (0, 0, -1), (1, 0, 1)}.

1, 1, 4, 11, 34, 123, 435, 1533, 5892, 22237, 84367, 332331, 1306500, 5142079, 20652446, 83135547, 334935274, 1364559971, 5580387419, 22840235561, 94098748404, 389138417389, 1611015331384, 6696438808173, 27926143286144, 116611087095741, 488218244457241, 2049513930152671, 8615627892995420

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, 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: A112272 A149234 A149235 * A135919 A034755 A297608

Adjacent sequences: A149233 A149234 A149235 * A149237 A149238 A149239

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved