A151110 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, 0), (0, 1, 0), (1, 0, 0), (1, 1, 1)}

1, 3, 11, 45, 187, 821, 3639, 16445, 75299, 347041, 1616443, 7561899, 35593793, 168297467, 798480657, 3803381005, 18162203269, 86978159921, 417499394667, 2008036165615, 9677714027555, 46716157888291, 225876896720627, 1093684863896891, 5302402827561317, 25739324193084863, 125081068214983069

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, 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: A144637 A369839 A151109 * A151111 A292278 A151112

Adjacent sequences: A151107 A151108 A151109 * A151111 A151112 A151113

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved