A149627 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, -1), (1, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 67, 251, 1111, 4665, 20973, 91881, 418061, 1883901, 8689577, 39803389, 185200353, 859052395, 4030363759, 18861149603, 89009182663, 419555644567, 1990687934283, 9435960182483, 44955830165287, 214099993546451, 1023901137320951, 4895129136430227, 23481373814033759, 112635951456766219

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A149624 A149625 A149626 * A149628 A149629 A149630

Adjacent sequences: A149624 A149625 A149626 * A149628 A149629 A149630

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved