A150075 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, 0, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 6, 18, 66, 217, 814, 2854, 10830, 39020, 150669, 551717, 2141530, 7965570, 31023777, 116458802, 455951716, 1722943694, 6760597014, 25718083565, 101077038578, 386268666289, 1521609833822, 5835919019436, 23017212465986, 88600412710513, 349777565501508, 1350086327973194, 5336502456184033

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + 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: A108066 A052863 A037128 * A150076 A150077 A173385

Adjacent sequences: A150072 A150073 A150074 * A150076 A150077 A150078

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved