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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).
3
0, 1, 12, 456, 54216, 6932916, 1069256400, 170663949024, 29130191148240, 5115288488816760, 927446504770571520, 171486284915686699620, 32295496327107026335392, 6164943698859825359296740, 1190940852937573264531168944, 232287567721717805821704554232
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * 6^(3*n) / n, where c = 0.000020280187096503586851533... . - Vaclav Kotesovec, Oct 14 2016
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 *)
CROSSREFS
Cf. A048116.
Sequence in context: A202799 A121348 A239365 * A226358 A225796 A112363
KEYWORD
nonn,walk
AUTHOR
Alois P. Heinz, Oct 07 2016
STATUS
approved