A150064 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, -1), (1, -1, 0), (1, 0, 0), (1, 1, 0)}.

1, 2, 6, 18, 63, 226, 870, 3365, 13697, 55917, 235493, 991616, 4287439, 18531073, 81564725, 358571572, 1602215627, 7152092988, 32311542880, 145790688544, 665088946686, 3031019012280, 13931089053070, 63959612298966, 295972677188241, 1368411197961976, 6366687361131662, 29595489020917756

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, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A150061 A150062 A150063 * A148463 A150065 A150066

Adjacent sequences: A150061 A150062 A150063 * A150065 A150066 A150067

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved