A148114 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, 0, 1), (0, -1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 10, 29, 88, 287, 959, 3339, 11879, 43425, 161638, 612803, 2358591, 9197282, 36298599, 144732075, 582562293, 2364494107, 9670613493, 39824362354, 165041369538, 687914981583, 2882579631664, 12138167876153, 51343558159145, 218092918948182, 930013276848835, 3980284917713303

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, -1 + k, -1 + n] + aux[1 + i, 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: A005505 A262592 A187255 * A135334 A182486 A000995

Adjacent sequences: A148111 A148112 A148113 * A148115 A148116 A148117

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved