A148938 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, 0, 0), (-1, 0, 1), (0, 0, -1), (0, 1, 1), (1, -1, 0)}.

1, 1, 3, 9, 29, 96, 350, 1292, 4899, 18831, 74312, 296745, 1198823, 4886726, 20140263, 83681564, 350091692, 1473326213, 6238321647, 26559287386, 113604606928, 487942278945, 2104187218979, 9108794276136, 39565656120954, 172386792190214, 753267792657033, 3300723149321924, 14500845883582327

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A289804 A071736 A286955 * A082306 A124431 A071740

Adjacent sequences: A148935 A148936 A148937 * A148939 A148940 A148941

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved