cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-1 of 1 results.

A103691 Triangle read by rows: T(n,k) = number of bracelets of n beads (necklaces that can be flipped over) with exactly two colors and k white beads, for which the length (or abs value) of sum of the position vectors of the white beads are different.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 3, 3, 1, 1, 3, 4, 4, 3, 1, 1, 4, 4, 6, 4, 4, 1, 1, 4, 7, 10, 10, 7, 4, 1, 1, 5, 7, 11, 11, 11, 7, 5, 1, 1, 5, 10, 20, 26, 26, 20, 10, 5, 1, 1, 6, 10, 16, 18, 20, 18, 16, 10, 6, 1, 1, 6, 14, 34, 57, 74, 74, 57, 34, 14, 6, 1, 1, 7, 14, 33, 44, 53, 53, 53, 44, 33
Offset: 2

Views

Author

Wouter Meeussen, Feb 12 2005

Keywords

Comments

Offset is 2, since exactly two colors are required, ergo at least two beads.
T[2n,n] equals A077078. Row sums equal A103692.

Examples

			T[8,3]=4 because of the 5 bracelets {1,1,1,0,0,0,0,0}, {0,0,0,0,1,0,1,1}, {0,0,0,1,0,0,1,1},{0,0,0,1,0,1,0,1} and {0,0,1,0,0,1,0,1}, the third and the fourth have equal absolute vector sums, length 1.
Table starts as:
  1;
  1,1;
  1,2,1;
  1,2,2,1;
  ...
		

Crossrefs

Programs

  • Mathematica
    Needs[DiscreteMath`NewCombinatorica`]; f[bi_]:=DeleteCases[bi*Range[Length[bi]], 0]; vec[li_, l_]:= Abs[Plus@@ N[Exp[2*Pi*I*f[li]/l], 24]]; Table[Length[Union[(vec[ #, n]&)/@ ListNecklaces[n, Join[1+0*Range[i], 0*Range[n-i]], Dihedral], SameTest->(Abs[ #1-#2]<10^-18&)]], {n, 2, 16}, {i, 1, n-1}]
Showing 1-1 of 1 results.