A149062 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), (-1, 1, 1), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 11, 39, 155, 639, 2685, 11659, 51415, 230181, 1042189, 4767683, 21999127, 102190479, 477697337, 2244781469, 10597607643, 50235495945, 238990143211, 1140630445769, 5459534054075, 26199537164759, 126021641896975, 607457870715145, 2933760183673987, 14193780496451361, 68781552133917699

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A132889 A245390 A149061 * A066979 A333548 A136775

Adjacent sequences: A149059 A149060 A149061 * A149063 A149064 A149065

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved