A148900 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, 1), (0, 1, -1), (0, 1, 1), (1, -1, 1)}.

1, 1, 3, 8, 31, 107, 411, 1571, 6385, 25550, 105633, 440141, 1861495, 7884724, 33865441, 146240291, 635169909, 2770387952, 12169281883, 53629296915, 237212288003, 1053240729331, 4694825011413, 20975651110254, 93986248196520, 422331165521818, 1902349771392104, 8585384908904559, 38834978320859195

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148897 A148898 A148899 * A148901 A148902 A213092

Adjacent sequences: A148897 A148898 A148899 * A148901 A148902 A148903

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved