cp's OEIS Frontend

A108053 Maximum number of diagonals of a regular n-gon that meet at a non-center point.

%I A108053 #40 Sep 01 2023 08:19:38
%S A108053 0,0,2,2,2,3,2,3,2,4,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,7,2,3,2,3,2,5,
%T A108053 2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,7,2,3,2,3,2,5,2,3,2,3,
%U A108053 2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,7,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2
%N A108053 Maximum number of diagonals of a regular n-gon that meet at a non-center point.
%C A108053 Starting at a(13) = 2, sequence is periodic with period 30.
%H A108053 Paolo Xausa, <a href="/A108053/b108053.txt">Table of n, a(n) for n = 3..10000</a>
%H A108053 Bjorn Poonen and Michael Rubinstein, <a href="https://arxiv.org/abs/math/9508209">The Number of Intersection Points Made by the Diagonals of a Regular Polygon</a>, arXiv:math/9508209 [math.MG], 1995-2006.
%H A108053 <a href="/index/Pol#Poonen">Sequences formed by drawing all diagonals in regular polygon</a>
%H A108053 <a href="/index/Rec#order_30">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
%F A108053 From _Paolo Xausa_, May 11 2023: (Start)
%F A108053 a(n) = 0 if n <= 4.
%F A108053 For n > 4:
%F A108053 a(n) = 2 if n is odd or n = 6;
%F A108053 a(n) = 3 if n != 6 is even but not divisible by 6;
%F A108053 a(n) = 4 if n = 12;
%F A108053 a(n) = 5 if n != 12 is divisible by 6 but not 30;
%F A108053 a(n) = 7 if n is divisible by 30. (End)
%e A108053 In a 30-gon, there are non-center points where 7 diagonals meet, but no more than 7. Hence a(30) = 7.
%t A108053 LinearRecurrence[PadLeft[{1},30], {0, 0, 2, 2, 2, 3, 2, 3, 2, 4,2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 7, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 5},120] (* _Ray Chandler_, Aug 27 2015 - adapted to new data by _Paolo Xausa_, May 15 2023 *)
%t A108053 PadRight[{0,0,2,2,2,3,2,3,2,4},120,{2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,5,2,3,2,3,2,7,2,3}] (* _Harvey P. Dale_, Jun 20 2021 - adapted to new data by _Paolo Xausa_, May 15 2023 *)
%Y A108053 Cf. A006561, A007678.
%K A108053 easy,nonn
%O A108053 3,3
%A A108053 _David W. Wilson_, Jun 01 2005
%E A108053 a(4), a(6) and a(12) corrected by _Paolo Xausa_, May 11 2023