A149594 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), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 59, 219, 921, 3645, 15577, 64339, 280699, 1190139, 5237395, 22621313, 100613547, 440444631, 1970212053, 8714144825, 39234678923, 174950750695, 790927342669, 3549980796203, 16120209920735, 72748280770601, 331365813894369, 1502193234793423, 6864616274745073, 31240873355806595

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, 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: A149592 A149593 A230986 * A149595 A149596 A149597

Adjacent sequences: A149591 A149592 A149593 * A149595 A149596 A149597

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved