A150690 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, 0), (-1, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 26, 118, 438, 2068, 8166, 39240, 160688, 780200, 3273018, 15999030, 68284180, 335314092, 1449775962, 7142547625, 31195747268, 154066314055, 678400361461, 3356698148209, 14880029141896, 73734216202712, 328704931071284, 1630735149455340, 7304765510790510, 36274431142871498, 163164514434486246

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, 1 + k, -1 + n] + aux[1 + i, j, 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: A150688 A026660 A150689 * A150691 A150692 A150693

Adjacent sequences: A150687 A150688 A150689 * A150691 A150692 A150693

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved