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A335059 a(n) is the number of vertices in an n-gon formed by the straight line segments connecting vertex k to vertex 2k mod n. 4
3, 4, 6, 7, 11, 11, 14, 16, 26, 22, 36, 33, 40, 45, 61, 50, 76, 72, 81, 87, 111, 95, 131, 124, 137, 146, 176, 145, 201, 193, 208, 218, 256, 228, 286, 275, 294, 307, 351, 316, 386, 374, 395, 409, 461, 421, 501, 486, 511, 528, 586, 539, 631, 615, 642, 660, 726 (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.

Select the row in the table below for which d = n mod m. Then a(n) = (a*n^2+bn+c)/denom.

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

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

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

|           1, 5 |  6 | 5 |   0 |  19 |    24 |

|              3 |  6 | 5 | -16 |  75 |    24 |

|          2, 10 | 12 | 5 | -18 |  64 |    24 |

|           4, 8 | 12 | 5 | -18 |  88 |    24 |

|              0 | 60 | 5 | -34 |  24 |    24 |

|  6, 18, 42, 54 | 60 | 5 | -34 | 192 |    24 |

| 12, 24, 36, 48 | 60 | 5 | -34 | 216 |    24 |

|             30 | 60 | 5 | -34 |   0 |    24 |

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

PROG

(PARI) bc=[[5, 0, 19, 24], [5, -16, 75, 24], [5, -18, 64, 24], [5, -18, 88, 24], [5, -34, 24, 24], [5, -34, 192, 24], [5, -34, 216, 24], [5, -34, 0, 24]];

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)=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), A335058 (edges), A335129 (distinct lines).

Sequence in context: A194095 A064404 A294488 * A047514 A011975 A202112

Adjacent sequences:  A335056 A335057 A335058 * A335060 A335061 A335062

KEYWORD

nonn

AUTHOR

Lars Blomberg, May 24 2020

STATUS

approved

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Last modified June 12 18:42 EDT 2021. Contains 344959 sequences. (Running on oeis4.)