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A242087
Number of balanced orbitals over an odd number of sectors.
3
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.
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
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