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.

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, 42504, 42504, 53130, 53130, 65780, 65780, 80730, 80730

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

Amiram Eldar, Table of n, a(n) for n = 10..10000

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

Vladimir 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

Sum_{n>=10} 1/a(n) = 5/2. - Amiram Eldar, Nov 18 2025

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, A194005.

Sequence in context: A034695 A339338 A198340 * A188273 A185786 A341245

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

More terms from Amiram Eldar, Nov 18 2025

Status

approved