A149360 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, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 44, 155, 615, 2411, 9970, 40891, 174401, 740721, 3229916, 14042215, 62258717, 275471949, 1237417112, 5550593831, 25195430116, 114255398662, 523102262154, 2393378795877, 11036621432426, 50872385276570, 236019676201247, 1094752434489828, 5105652630068450, 23809462275320561

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, j, -1 + k, -1 + n] + aux[-1 + i, 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: A320643 A060897 A005190 * A149361 A149362 A149363

Adjacent sequences: A149357 A149358 A149359 * A149361 A149362 A149363

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved