A148852 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, 0), (1, -1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 8, 28, 91, 339, 1219, 4729, 17967, 72051, 284889, 1168359, 4742941, 19784801, 81931257, 346432579, 1457019579, 6229024211, 26524446504, 114437092724, 492263548721, 2140219854313, 9284528309060, 40632801423118, 177536118818556, 781408211355630, 3435232456516649, 15195467329981059

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148849 A148850 A148851 * A148853 A148854 A148855

Adjacent sequences: A148849 A148850 A148851 * A148853 A148854 A148855

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved