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A140106 Number of noncongruent diagonals in a regular n-gon. 4
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

LINKS

Table of n, a(n) for n=1..76.

W. Bomfim, Double-star corresponding to the partition [3,7]

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Index entries for sequences related to trees

FORMULA

For n > 1, 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

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[1]=0; a[n_?OddQ] := (n-3)/2; a[n_] := n/2-1; Array[a, 100] (* Jean-Fran├žois 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.

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

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Last modified November 24 00:27 EST 2017. Contains 295164 sequences.