A272135 Numbers of ways of placing the numbers 1, ..., n on a circle (not counting rotations and reflections) such that for each s in {1, ..., n(n+1)/2}, there exists a connected subset S of the circle such that the numbers covered by S add up to s.

1, 1, 1, 1, 2, 10, 41, 126, 537, 3956, 19776, 76340, 388047, 2775155, 15013424, 54188455, 272147013

Offset: 0

Author

Jens Voß, Apr 21 2016

Keywords

• nonn
• more

Examples

			Out of the 3 essentially different arrangements (1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 2, 4) of four points on a circle, only (1, 2, 3, 4) and (1, 3, 2, 4) yield all sums in {1, ..., 10}, so a(4) = 2.
		

Links

• Mathematics Stack Exchange, Placing the integers {1,2,...,n} on a circle (for n>1) in some special order

Programs

Mathematica

ok[w_] := Block[{v = Join[w,w], n = Length@w}, n(n+1)/2 == Length@ Union@ Flatten@ Table[ Total@ Take[v, {i, i+k}], {i,n}, {k, 0, n-1}]]; a[n_] := If[n<3, 1, Sum[ Length@ Select[ Permutations@ Complement[ Range@n, e], ok@ Join[e, #] &], {e, Flatten[ Table[{a,1,b}, {a,2,n}, {b,a+1,n}], 1]}]]; a /@ Range[0, 9] (* Giovanni Resta, Apr 21 2016 *)

Extensions

a(15) from Giovanni Resta, Apr 21 2016

a(16) from Giovanni Resta, Apr 22 2016