OFFSET
0,5
COMMENTS
For the combinatorial definitions see A232500. An orbital is balanced if its integral is 0. The integral of an orbital w over n sectors is sum(1<=k<=n, sum(1<=i<=k, w(i))) where w(i) are the jumps of the orbital represented by -1, 0, 1.
FORMULA
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}];
n=0; f=0; Print[1]; Print[1]; While[n<16, n++; f=1-f; If[OddQ[f*n], Print[0], p=Join[-Take[o, n], {f}, Take[o, n-f]]; c=0; Do[If[Accumulate[Accumulate[p]][[-1]]==0, c++]; p=np[p], {(2*n+1-f)!/(2*n!^2)}]; Print[2*c]]; n=n-f]
(* Hans Havermann, May 10 2014 *)
PROG
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Peter Luschny, Apr 29 2014
EXTENSIONS
More terms from Hans Havermann, May 10 2014
a(35), a(36) from Hans Havermann, May 23 2014
STATUS
approved