A149467 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, 0, 0), (0, -1, 1), (0, 1, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 4, 13, 54, 211, 900, 3864, 17140, 76671, 348895, 1600022, 7409257, 34544983, 162084082, 764339635, 3621694614, 17226889200, 82230946010, 393754786454, 1890628315375, 9100266393559, 43901797951237, 212213506746634, 1027668820749187, 4984935211875089, 24216880591986593, 117808667147917938

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[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A006604 A082570 A145208 * A149468 A149469 A229182

Adjacent sequences: A149464 A149465 A149466 * A149468 A149469 A149470

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved