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A189980 a(n) is the number of incongruent two-color bracelets of n beads, 10 from them are black (A005515), having a diameter of symmetry. 4
1, 1, 6, 6, 21, 21, 56, 56, 126, 126, 252, 252, 462, 462, 792, 792, 1287, 1287, 2002, 2002, 3003, 3003, 4368, 4368, 6188, 6188, 8568, 8568, 11628, 11628, 15504, 15504, 20349, 20349, 26334, 26334, 33649, 33649 (list; graph; refs; listen; history; text; internal format)
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.

REFERENCES

H. Gupta, Enumeration of incongruent cyclic k-gons, Indian J. Pure and Appl. Math., 10 (1979), no.8, 964-999.

LINKS

Table of n, a(n) for n=10..47.

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

Cf. A005515, A032282, A008805, A058187, A189976.

Sequence in context: A298936 A034695 A198340 * A188273 A185786 A178822

Adjacent sequences:  A189977 A189978 A189979 * A189981 A189982 A189983

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 14 15:21 EST 2019. Contains 329126 sequences. (Running on oeis4.)