The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A140106 Number of noncongruent diagonals in a regular n-gon. 15
 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Number of double-stars (diameter 3 trees) with n nodes. For n >= 3, number of partitions of n-2 into two parts. - Washington Bomfim, Feb 12 2011 Number of roots of the n-th Bernoulli polynomial in the left half-plane. - Michel Lagneau, Nov 08 2012 From Gus Wiseman, Oct 17 2020: (Start) Also the number of 3-part non-strict integer partitions of n - 1. The Heinz numbers of these partitions are given by A285508. The version for partitions of any length is A047967, with Heinz numbers A013929. The a(4) = 1 through a(15) = 6 partitions are (A = 10, B = 11, C = 12):   111  211  221  222  322  332  333  433  443  444  544  554             311  411  331  422  441  442  533  552  553  644                       511  611  522  622  551  633  661  662                                 711  811  722  822  733  833                                           911  A11  922  A22                                                     B11  C11 (End) LINKS Washington Bomfim, Double-star corresponding to the partition [3,7] Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA For n > 1, a(n) = floor((n-2)/2), otherwise 0. - Washington Bomfim, Feb 12 2011 G.f.: x^4/(1-x-x^2+x^3). - Colin Barker, Jan 31 2012 For n > 1, a(n) = floor(A129194(n - 1)/A022998(n)). - Paul Curtz, Jul 23 2017 a(n) = A001399(n-3) - A001399(n-6). Compare to A007997(n) = A001399(n-3) + A001399(n-6). - Gus Wiseman, Oct 17 2020 EXAMPLE The square (n=4) has two congruent diagonals; so a(4)=1. The regular pentagon also has congruent diagonals; so a(5)=1. Among all the diagonals in a regular hexagon, there are two noncongruent ones; hence a(6)=2, etc. MAPLE with(numtheory): for n from 1 to 80 do:it:=0: y:=[fsolve(bernoulli(n, x) , x, complex)] : for m from 1 to nops(y) do : if Re(y[m])<0 then it:=it+1:else fi:od: printf(`%d, `, it):od: MATHEMATICA a=0; a[n_?OddQ] := (n-3)/2; a[n_] := n/2-1; Array[a, 100] (* Jean-François Alcover, Nov 17 2015 *) PROG (PARI) a(n)=if(n>1, n\2-1, 0) \\ Charles R Greathouse IV, Oct 16 2015 CROSSREFS Essentially the same as A004526. Cf. A000554, A022998, A129194. A001399(n-3) = A069905(n) = A211540(n+2) counts 3-part partitions. Cf. A007304, A007997, A013929, A047967, A235451, A285508, A321773. Sequence in context: A076938 A080513 A004526 * A123108 A008619 A110654 Adjacent sequences:  A140103 A140104 A140105 * A140107 A140108 A140109 KEYWORD nonn,easy AUTHOR Andrew McFarland, Jun 03 2008 EXTENSIONS More terms from Joseph Myers, Sep 05 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 26 02:05 EDT 2022. Contains 356986 sequences. (Running on oeis4.)