A149048 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, 1, 0), (0, 1, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 3, 10, 39, 144, 615, 2488, 11080, 47401, 216326, 958515, 4449062, 20178691, 94826467, 437279311, 2074031303, 9683449511, 46256188985, 218045307657, 1047393986003, 4974855688358, 24004438387183, 114714186654017, 555549959677201, 2668229855852317, 12961512432099073, 62511691341765926

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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A298940 A327847 A111749 * A149049 A149050 A300974

Adjacent sequences: A149045 A149046 A149047 * A149049 A149050 A149051

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved