OFFSET
10,3
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).
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
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 *)
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