A335058 - OEIS

%I #5 May 25 2020 23:27:17

%S 3,5,9,10,19,20,24,31,49,41,69,66,76,90,119,99,149,145,158,176,219,

%T 190,259,251,270,295,349,296,399,390,412,441,509,459,569,556,584,620,

%U 699,637,769,755,786,826,919,848,999,981,1018,1065,1169,1086,1259,1240

%N a(n) is the number of edges in an n-gon formed by the straight line segments connecting vertex k to vertex 2k mod n.

%C See A335057 for illustrations.

%H Lars Blomberg, <a href="/A335058/b335058.txt">Table of n, a(n) for n = 3..270</a>

%F Empirically for n <= 270.

%F For n > 3 select the row in the table below for which d = n mod m. Then a(n) = (a*n^2+b*n+c)/denom.

%F +=============================================+

%F |              d |  m | a |   b |   c | denom |

%F +---------------------------------------------+

%F |           1, 5 |  6 | 5 |   0 | -17 |    12 |

%F |              3 |  6 | 5 | -16 |  27 |    12 |

%F |          2, 10 | 12 | 5 | -15 |  22 |    12 |

%F |           4, 8 | 12 | 5 | -15 |  40 |    12 |

%F |              0 | 60 | 5 | -31 |   0 |    12 |

%F |  6, 18, 42, 54 | 60 | 5 | -31 | 126 |    12 |

%F | 12, 24, 36, 48 | 60 | 5 | -31 | 144 |    12 |

%F |             30 | 60 | 5 | -31 | -18 |    12 |

%F +=============================================+

%o (PARI) bc=[[5,0,-17,12],[5,-16,27,12],[5,-15,22,12],[5,-15,40,12],[5,-31,0,12],[5,-31,126,12],[5,-31,144,12],[5,-31,-18,12]];

%o m=[[1,6,1],[5,6,1],[3,6,2],[2,12,3],[10,12,3],[4,12,4],[8,12,4],[0,60,5],[6,60,6],[18,60,6],[42,60,6],[54,60,6],[12,60,7],[24,60,7],[36,60,7],[48,60,7],[30,60,8]];

%o ix(n)=for(i=1,length(m),x=m[i];if(n%x[2]==x[1], return(x[3])));-1

%o a(n)=if(n==3,return(3));x=bc[ix(n)];(x[1]*n^2+x[2]*n+x[3])/x[4]

%o vector(200,x,a(x+2))

%Y Cf. A335057 (regions), A335059 (vertices), A335129 (distinct lines).

%K nonn

%O 3,1

%A _Lars Blomberg_, May 24 2020