A149910 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, 1, -1), (0, 0, -1), (0, 0, 1), (1, 0, 0)}.

1, 2, 5, 15, 45, 148, 502, 1766, 6432, 23753, 89949, 344107, 1337603, 5257450, 20867047, 83699338, 337925520, 1376164889, 5635244713, 23226831515, 96241844903, 400714413394, 1676717147085, 7042517238362, 29708580384864, 125739464072768, 534100530069694, 2275729997688530, 9724986583465393

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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A206302 A149908 A149909 * A149911 A148357 A149912

Adjacent sequences: A149907 A149908 A149909 * A149911 A149912 A149913

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved