A242087 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

	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], {(2n+1)!/(2n!^2)}]; Print[2c], {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 August 31 08:34 EDT 2024. Contains 375560 sequences. (Running on oeis4.)