A149404 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, 1), (-1, 0, 0), (-1, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 52, 177, 807, 3041, 14268, 56590, 270028, 1106952, 5339922, 22402560, 108879743, 464602037, 2270119906, 9813344344, 48139440999, 210239624137, 1034441748942, 4555286272410, 22466061317387, 99610665420191, 492185173300521, 2194832280561287, 10861273254989284, 48671943604817077

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, j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A303392 A149403 A127866 * A149405 A149406 A149407

Adjacent sequences: A149401 A149402 A149403 * A149405 A149406 A149407

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved