A189976 a(n) is the number of incongruent two-color bracelets of n beads, 8 of them black (A005514), having a diameter of symmetry.
1, 1, 5, 5, 15, 15, 35, 35, 70, 70, 126, 126, 210, 210, 330, 330, 495, 495, 715, 715, 1001, 1001, 1365, 1365, 1820, 1820, 2380, 2380, 3060, 3060, 3876, 3876, 4845, 4845, 5985, 5985, 7315, 7315, 8855, 8855, 10626
Offset: 8
Links
- Vincenzo Librandi, Table of n, a(n) for n = 8..1000
- H. 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 (1,4,-4,-6,6,4,-4,-1,1).
Programs
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Magma
[Binomial(Floor(n/2),4): n in[8..60]]; // Vincenzo Librandi, Aug 10 2014
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Maple
A189976 :=proc(n): binomial(floor(n/2),4) end: seq(A189976(n), n=8..48); # Johannes W. Meijer, Aug 15 2011
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Mathematica
Module[{c=Binomial[Range[4,30],4]},Riffle[c,c]] (* Harvey P. Dale, Aug 09 2014 *) Table[(Binomial[Floor[n/2], 4]), {n, 8, 40}] (* Vincenzo Librandi, Aug 10 2014 *)
Formula
a(n) = C(floor(n/2),4).
a(n+5) = A194005(n,n-4). [Johannes W. Meijer, Aug 15 2011]
G.f.: -x^8/((x-1)^5*(x+1)^4). [Colin Barker, Feb 06 2013]
Extensions
Data added and link corrected by Johannes W. Meijer, Aug 15 2011
Comments