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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. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)