A149620 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, 0, 1), (1, -1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 65, 243, 1063, 4339, 19235, 82027, 367879, 1609567, 7285259, 32414039, 147766247, 665264845, 3049902451, 13851990637, 63793187083, 291697457499, 1348385428421, 6198632275193, 28743077414259, 132708458095627, 617006990481141, 2858981290764263, 13322896279147479, 61919267605858555

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A149618 A323793 A149619 * A149621 A149622 A247281

Adjacent sequences: A149617 A149618 A149619 * A149621 A149622 A149623

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved