A148344 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, 0), (-1, 0, 0), (-1, 1, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 2, 5, 15, 39, 127, 405, 1330, 4478, 15574, 54337, 194625, 699722, 2558633, 9423633, 35049948, 131371020, 495572962, 1882605608, 7196722963, 27626157357, 106690061753, 413630954817, 1610691764954, 6298169581271, 24703968025232, 97266195844071, 384155216430075, 1521472349416453, 6044403219103030

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A280064 A148342 A148343 * A148345 A148346 A148347

Adjacent sequences: A148341 A148342 A148343 * A148345 A148346 A148347

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved