A149617 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, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 65, 231, 1049, 4011, 18485, 74073, 344159, 1420619, 6640395, 27983731, 131369483, 562216845, 2647935169, 11468400275, 54152874967, 236788885161, 1120433948881, 4937654152517, 23404568421231, 103817747202309, 492825352426061, 2198232231222405, 10448373626637379, 46827872771777471

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, 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: A149616 A189945 A066886 * A149618 A323793 A149619

Adjacent sequences: A149614 A149615 A149616 * A149618 A149619 A149620

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved