A242087 Number of balanced orbitals over an odd number of sectors.

1, 0, 6, 6, 36, 88, 376, 1096, 4476, 14200, 57284, 190206, 764812, 2615268, 10499504, 36677626, 147110276, 522288944

Offset: 0

Author

Peter Luschny, May 04 2014

Keywords

• nonn
• more

Comments

See A241810 and A232500 for the combinatorial definitions.

Programs

Mathematica

np[z_]:=Module[{i,j},For[i=Length[z],i>1&&z[[i-1]]>=z[[i]],i--]; For[j=Length[z],z[[j]]<=z[[i-1]],j--]; Join[Take[z,i-2],{z[[j]]}, Reverse[Drop[ReplacePart[z,z[[i-1]],j],i-1]]]]; o=Table[1,{16}];
Print[1]; Do[p=Join[-Take[o,n],{0},Take[o,n]]; c=0; Do[If[Accumulate[Accumulate[p]][[-1]]==0,c++]; p=np[p],{(2*n+1)!/(2*n!^2)}]; Print[2*c],{n,16}]
(* Hans Havermann, May 10 2014 *)

Sage

def A242087(n):
    if n == 0: return 1
    A = 0; T = [0]
    for i in (1..n):
        T.append(-1); T.append(1)
    for p in Permutations(T):
        P = 0; S = 0
        for k in (0..2*n):
            P += p[k]; S += P
        if S == 0: A += 1
    return A
[A242087(n) for n in (0..10)]

Formula

a(n) = A241810(2*n+1).

Extensions

More terms from Hans Havermann, May 10 2014

a(17) from Hans Havermann, May 23 2014