A149753 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, 1), (1, 0, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 83, 321, 1591, 6703, 33373, 147727, 736945, 3364931, 16801887, 78306089, 391203703, 1849547589, 9242836257, 44158627031, 220716999275, 1062867840851, 5313123521945, 25742526291623, 128692783682713, 626548287495809, 3132411437550179, 15309626547447817, 76542561918362105

Offset

0,3

Links

Table of n, a(n) for n=0..26.

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A188231 A023253 A149752 * A149754 A149755 A365878

Adjacent sequences: A149750 A149751 A149752 * A149754 A149755 A149756

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved