A149859 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, 0), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 2, 5, 13, 38, 124, 424, 1476, 5196, 18925, 70739, 268198, 1021458, 3934866, 15386445, 60817590, 241493597, 963318241, 3874403554, 15708096480, 63979516337, 261305467446, 1071976962325, 4422643793057, 18324387536241, 76103216963727, 316881010419051, 1324459171412129, 5556007355104909

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A149858 A148303 A148304 * A000800 A149860 A006823

Adjacent sequences: A149856 A149857 A149858 * A149860 A149861 A149862

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved