A277262 Number of walks on cubic lattice starting at (1,1,1), ending at (n,n,n), remaining in the first (nonnegative) octant and using steps (0,-1,2), (0,2,-1), (-1,0,2), (2,0,-1), (-1,2,0), and (2,-1,0).

0, 1, 12, 456, 54216, 6932916, 1069256400, 170663949024, 29130191148240, 5115288488816760, 927446504770571520, 171486284915686699620, 32295496327107026335392, 6164943698859825359296740, 1190940852937573264531168944, 232287567721717805821704554232

Offset: 0

Author

Alois P. Heinz, Oct 07 2016

Keywords

• nonn
• walk

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A048116.

Programs

Maple

g():= combinat[permute]([0, -1, 2]):
b:= proc(l) option remember; `if`(l=[1$3], 1, add((p->
      `if`(p[1]<0, 0, b(p)))(sort(l-x)), x=g()))
    end:
a:= n-> b([n$3]):
seq(a(n), n=0..20);

Mathematica

g = Permutations[{0, -1, 2}];
b[l_] := b[l] = If[l == {1, 1, 1}, 1, Sum[Function[p, If[p[[1]] < 0, 0, b[p]]][Sort[l - x]], {x, g}]];
a[n_] := b[{n, n, n}];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 29 2017, translated from Maple *)

Formula

a(n) ~ c * 6^(3*n) / n, where c = 0.000020280187096503586851533... . - Vaclav Kotesovec, Oct 14 2016