A077079 Number of inequivalent bracelets from A006840 with the additional equivalence condition that subsets of 1-beads whose position vectors add to zero can be removed. Different values of vector sums of (-1)^(k/n) with k taking n values in 1..2n up to rotation and reflection.

1, 2, 3, 6, 11, 20, 53, 130, 199, 784, 2135, 2649, 15695, 43085, 32764

Offset: 1

Author

Wouter Meeussen, Oct 27 2002

Keywords

• hard
• more
• nonn

Comments

At n=15 the sequence decreases because of the large number of divisors of 30.

Crossrefs

Identical to A077078 up to n=9. Cf. A006840.

Programs

Mathematica

lowest[li_] := First[Sort[Join[NestList[RotateRight, li, 2n-1], NestList[RotateRight, 1-li, 2n-1], NestList[RotateRight, Reverse@li, 2n-1], NestList[RotateRight, 1-Reverse@li, 2n-1]]]]; ker[n_, k_] := Flatten[Table[Join[{1}, 0Range[ -1+2n/k]], {k}]]; ingekort[li_] := Module[{temp, divi}, len=Length[li]; temp=li-(liRotateRight[li, len/2]); divi=First/@FactorInteger[len]; Table[d=divi[[s]]; k=ker[len/2, d]; temp=Fold[kort[ #1, #2]&, temp, NestList[RotateRight, k, len/d-1]], {s, Length[divi], 2, -1}]; lowest[temp]]; kort[q_, k_] := If[(q.k>=Floor[d/2+1])&&(q.RotateRight[k-kq, len/2]===0), q-kq+RotateRight[k-kq, len/2], q]; Length[inequiv=Union[ingekort/@ListOfBraceletsA006840]]