A189980 a(n) is the number of incongruent two-color bracelets of n beads, 10 from them are black (A005515), having a diameter of symmetry.

1, 1, 6, 6, 21, 21, 56, 56, 126, 126, 252, 252, 462, 462, 792, 792, 1287, 1287, 2002, 2002, 3003, 3003, 4368, 4368, 6188, 6188, 8568, 8568, 11628, 11628, 15504, 15504, 20349, 20349, 26334, 26334, 33649, 33649

Offset: 10

Author

Vladimir Shevelev, May 03 2011

Keywords

• nonn
• easy

Comments

For n >= 11, a(n-1) is the number of incongruent two-color bracelets of n beads, 11 from them are black (A032282), having a diameter of symmetry.

Links

• Hansraj Gupta, Enumeration of incongruent cyclic k-gons, Indian J. Pure and Appl. Math., 10 (1979), no. 8, 964-999.
• V. Shevelev, A problem of enumeration of two-color bracelets with several variations, arXiv:0710.1370 [math.CO], 2007-2011.
• Index entries for linear recurrences with constant coefficients, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).

Crossrefs

Cf. A005515, A032282, A008805, A058187, A189976.

Programs

Maple

A189980 :=proc(n): binomial(floor(n/2),5) end: seq(A189980(n), n=10..47); # Johannes W. Meijer, Aug 15 2011

Mathematica

Table[Binomial[Floor[n/2],5],{n,10,50}] (* Harvey P. Dale, Oct 06 2017 *)

Formula

a(n) = binomial(floor(n/2), 5). [Typo fixed by Colin Barker, Feb 07 2013]

a(n+6) = A194005(n, n-5). - Johannes W. Meijer, Aug 15 2011

G.f.: x^10/((x-1)^6*(x+1)^5). - Colin Barker, Feb 07 2013

Extensions

Data added and link corrected by Johannes W. Meijer, Aug 15 2011