A150681 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, 1)}.

1, 2, 8, 26, 114, 421, 1942, 7636, 36085, 147350, 705918, 2955504, 14287308, 60890684, 296162054, 1279163091, 6248661396, 27271297636, 133652855104, 588213884991, 2890105470667, 12807642645672, 63057715639092, 281068485457650, 1386149866336724, 6209143577848650, 30664347303590324, 137946282290761229

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, -1 + 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: A150678 A150679 A150680 * A150682 A303478 A150683

Adjacent sequences: A150678 A150679 A150680 * A150682 A150683 A150684

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved