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A335058 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. 4
3, 5, 9, 10, 19, 20, 24, 31, 49, 41, 69, 66, 76, 90, 119, 99, 149, 145, 158, 176, 219, 190, 259, 251, 270, 295, 349, 296, 399, 390, 412, 441, 509, 459, 569, 556, 584, 620, 699, 637, 769, 755, 786, 826, 919, 848, 999, 981, 1018, 1065, 1169, 1086, 1259, 1240 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

See A335057 for illustrations.

LINKS

Lars Blomberg, Table of n, a(n) for n = 3..270

FORMULA

Empirically for n <= 270.

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.

+=============================================+

|              d |  m | a |   b |   c | denom |

+---------------------------------------------+

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

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

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

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

|              0 | 60 | 5 | -31 |   0 |    12 |

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

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

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

+=============================================+

PROG

(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]];

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]];

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

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

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

CROSSREFS

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

Sequence in context: A063038 A236309 A304588 * A066769 A323765 A270780

Adjacent sequences:  A335055 A335056 A335057 * A335059 A335060 A335061

KEYWORD

nonn

AUTHOR

Lars Blomberg, May 24 2020

STATUS

approved

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Last modified August 4 00:29 EDT 2021. Contains 346441 sequences. (Running on oeis4.)