A148343 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, -1, 1), (-1, 1, 0), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 5, 15, 39, 127, 405, 1318, 4466, 15592, 53968, 193558, 699208, 2540930, 9383647, 34949626, 130634061, 493419324, 1876247580, 7158355193, 27508780199, 106273910202, 411872196856, 1603670034112, 6273367974987, 24604878644058, 96858159552413, 382698785465422, 1515837529151695, 6020179697966447

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A059840 A280064 A148342 * A148344 A148345 A148346

Adjacent sequences: A148340 A148341 A148342 * A148344 A148345 A148346

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved