A151040 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, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0)}.

1, 3, 9, 33, 129, 501, 2078, 8801, 36943, 160485, 704591, 3069821, 13661138, 61186869, 272378367, 1230330551, 5581589774, 25197063385, 114975285714, 526286613363, 2399288969358, 11028850184643, 50817241344590, 233362192847828, 1078701075478305, 4995546879309872, 23069300401218194, 107104618408678372

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A049151 A254036 A151039 * A151041 A151042 A087289

Adjacent sequences: A151037 A151038 A151039 * A151041 A151042 A151043

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved