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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
OFFSET
3,1
COMMENTS
See A335057 for illustrations.
LINKS
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: A064404 A294488 A364341 * A047514 A345716 A011975
KEYWORD
nonn
AUTHOR
Lars Blomberg, May 24 2020
STATUS
approved