A148911 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, 0, 1), (-1, 1, 1), (1, -1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 8, 32, 109, 473, 1825, 8230, 34068, 157238, 679798, 3185677, 14179452, 67157892, 305141027, 1456515990, 6719210749, 32262493470, 150566769960, 726300897107, 3420426006425, 16560687508248, 78556938942381, 381506190097330, 1820392982010714, 8863002766079997, 42496976025533422

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148908 A148909 A148910 * A148912 A148913 A148914

Adjacent sequences: A148908 A148909 A148910 * A148912 A148913 A148914

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved