A149746 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), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 79, 321, 1495, 6573, 31065, 141617, 676833, 3152859, 15182849, 71728255, 347298041, 1656855433, 8054826535, 38702146611, 188738813863, 911762020051, 4457392471811, 21623357018245, 105923703041785, 515568844677031, 2529748799040933, 12346663707662589, 60666248855162981, 296751342552120827

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A211474 A149744 A149745 * A149747 A149748 A151494

Adjacent sequences: A149743 A149744 A149745 * A149747 A149748 A149749

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved