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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See A241810 and A232500 for the combinatorial definitions. LINKS 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: A176861 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

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Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)