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

8,3

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

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).

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

Cf. A005514, A032281, A008805, A058187.

Sequence in context: A196060 A147266 A147152 * A188272 A104551 A100746

Adjacent sequences: A189973 A189974 A189975 * A189977 A189978 A189979

Keyword

nonn,easy

Author

Vladimir Shevelev, May 03 2011

Extensions

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

Status

approved