A149028 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), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 10, 32, 116, 450, 1727, 6837, 28060, 115565, 481369, 2040532, 8708109, 37423501, 162231361, 707449871, 3102033992, 13670214098, 60514683165, 269035757552, 1200266720500, 5373244040392, 24132690138088, 108682252595942, 490777845043766, 2221711774517289, 10079890026903695

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[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: A356499 A134952 A184436 * A174573 A126183 A174798

Adjacent sequences: A149025 A149026 A149027 * A149029 A149030 A149031

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved