

A140106


Number of noncongruent diagonals in a regular ngon.


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 doublestars (diameter 3 trees) with n nodes. For n >= 3, number of partitions of n2 into two parts.  Washington Bomfim, Feb 12 2011
Number of roots of the nth Bernoulli polynomial in the left halfplane.  Michel Lagneau, Nov 08 2012


LINKS

Table of n, a(n) for n=1..76.
W. Bomfim, Doublestar 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((n2)/2), otherwise 0.  Washington Bomfim, Feb 12 2011
G.f.: x^4/(1xx^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] := (n3)/2; a[n_] := n/21; Array[a, 100] (* JeanFrançois Alcover, Nov 17 2015 *)


PROG

(PARI) a(n)=if(n>1, n\21, 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



