A149991 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, 0, 1), (-1, 1, -1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 57, 207, 770, 2928, 11385, 44761, 178507, 717723, 2911567, 11889471, 48843018, 201708227, 836728300, 3485203920, 14568180657, 61093715901, 256943318442, 1083492074350, 4579868091028, 19401361515390, 82354213479878, 350222446183284, 1491926082298429, 6365617368220411

Offset

0,2

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A148412 A149989 A149990 * A149992 A134128 A119254

Adjacent sequences: A149988 A149989 A149990 * A149992 A149993 A149994

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved