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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
OFFSET
3,1
COMMENTS
See A335057 for illustrations.
LINKS
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
KEYWORD
nonn
AUTHOR
Lars Blomberg, May 24 2020
STATUS
approved