A149527 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), (-1, 1, -1), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 11, 53, 149, 737, 2351, 11629, 39687, 197311, 707205, 3519205, 13028739, 64938435, 246751393, 1230673099, 4768324351, 23797616719, 93712372299, 467883669379, 1866845588443, 9323722318663, 37619266504719, 187928984011715, 765483964644861, 3824704802081289, 15707739542521241

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, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A094107 A107009 A228865 * A201180 A109546 A104065

Adjacent sequences: A149524 A149525 A149526 * A149528 A149529 A149530

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved