A335129 a(n) is the number of distinct lines created inside an n-gon when connecting vertex k to vertex 2k mod n.

0, 1, 2, 2, 4, 5, 5, 7, 8, 8, 10, 11, 11, 13, 14, 14, 16, 17, 17, 19, 20, 20, 22, 23, 23, 25, 26, 26, 28, 29, 29, 31, 32, 32, 34, 35, 35, 37, 38, 38, 40, 41, 41, 43, 44, 44, 46, 47, 47, 49, 50, 50, 52, 53, 53, 55, 56, 56, 58, 59, 59, 61, 62, 62, 64, 65, 65

Offset

3,3

Comments

See A335057 for illustrations.

Links

Table of n, a(n) for n=3..69.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

a(n) = n - 3 - A079978(n) for n >= 4.

a(3) = 0, a(n) = n - 4 + sign(n mod 3) for n >= 4. - Wesley Ivan Hurt, Dec 29 2021

From Amiram Eldar, Feb 14 2026: (Start)

G.f.: ((1+x+x^3) * x^4)/((x-1)^2 * (1+x+x^2)).

Sum_{n>=4} (-1)^n/a(n) = Pi/(3*sqrt(3)) + log(2)/3. (End)

Mathematica

LinearRecurrence[{1, 0, 1, -1}, {0, 1, 2, 2, 4}, 100] (* Amiram Eldar, Feb 14 2026 *)

Prog

(PARI) a(n) = if(n < 4, 0, n - 3 - !(n % 3));  \\ Amiram Eldar, Feb 14 2026

Crossrefs

Cf. A079978.

Cf. A335057 (regions), A335058 (edges), A335059 (vertices).

Sequence in context: A118003 A159296 A277191 * A035632 A114701 A349464

Adjacent sequences: A335126 A335127 A335128 * A335130 A335131 A335132

Keyword

nonn,easy

Author

Lars Blomberg, May 24 2020

Status

approved