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A189976
a(n) is the number of incongruent two-color bracelets of n beads, 8 of them black (A005514), having a diameter of symmetry.
8
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
8,3
COMMENTS
For n >= 9, a(n-1) is the number of incongruent two-color bracelets of n beads, 9 from them are black (A032281), having a diameter of symmetry.
LINKS
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.
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]
MAPLE
A189976 :=proc(n): binomial(floor(n/2), 4) end: seq(A189976(n), n=8..48); # Johannes W. Meijer, Aug 15 2011
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 *)
PROG
(Magma) [Binomial(Floor(n/2), 4): n in[8..60]]; // Vincenzo Librandi, Aug 10 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Shevelev, May 03 2011
EXTENSIONS
Data added and link corrected by Johannes W. Meijer, Aug 15 2011
STATUS
approved