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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).

%I A277262 #13 Mar 29 2017 10:31:59
%S A277262 0,1,12,456,54216,6932916,1069256400,170663949024,29130191148240,
%T A277262 5115288488816760,927446504770571520,171486284915686699620,
%U A277262 32295496327107026335392,6164943698859825359296740,1190940852937573264531168944,232287567721717805821704554232
%N 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).
%H A277262 Alois P. Heinz, <a href="/A277262/b277262.txt">Table of n, a(n) for n = 0..400</a>
%F A277262 a(n) ~ c * 6^(3*n) / n, where c = 0.000020280187096503586851533... . - _Vaclav Kotesovec_, Oct 14 2016
%p A277262 g():= combinat[permute]([0, -1, 2]):
%p A277262 b:= proc(l) option remember; `if`(l=[1$3], 1, add((p->
%p A277262       `if`(p[1]<0, 0, b(p)))(sort(l-x)), x=g()))
%p A277262     end:
%p A277262 a:= n-> b([n$3]):
%p A277262 seq(a(n), n=0..20);
%t A277262 g = Permutations[{0, -1, 2}];
%t A277262 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}]];
%t A277262 a[n_] := b[{n, n, n}];
%t A277262 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Mar 29 2017, translated from Maple *)
%Y A277262 Cf. A048116.
%K A277262 nonn,walk
%O A277262 0,3
%A A277262 _Alois P. Heinz_, Oct 07 2016