A149880 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), (0, 0, 1), (0, 1, 0), (1, 1, -1)}.

1, 2, 5, 14, 43, 139, 466, 1603, 5627, 20070, 72521, 264861, 975996, 3623680, 13540852, 50880391, 192109376, 728417406, 2772227203, 10585500249, 40538986928, 155661286100, 599128863537, 2310961487189, 8931238199580, 34578129966890, 134089763743373, 520757083293026, 2025200075312320

Offset

0,2

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[i, j, -1 + 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: A149879 A366025 A366042 * A066351 A181496 A276989

Adjacent sequences: A149877 A149878 A149879 * A149881 A149882 A149883

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved