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

0,3

Comments

See A241810 and A232500 for the combinatorial definitions.

Links

Table of n, a(n) for n=0..17.

Formula

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

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 *)

Prog

(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)]

Crossrefs

Sequence in context: A377204 A245131 A038260 * A217978 A257626 A222340

Adjacent sequences: A242084 A242085 A242086 * A242088 A242089 A242090

Keyword

nonn,more

Author

Peter Luschny, May 04 2014

Extensions

More terms from Hans Havermann, May 10 2014

a(17) from Hans Havermann, May 23 2014

Status

approved