A335411 a(n) is the number of vertices formed by n-secting the angles of an equilateral triangle.

3, 7, 21, 25, 63, 67, 129, 133, 219, 199, 333, 337, 471, 475, 633, 637, 819, 823, 1029, 1009, 1263, 1267, 1521, 1525, 1803, 1807, 2109, 2113, 2439, 2419, 2793, 2797, 3171, 3175, 3573, 3577, 3999, 4003, 4449, 4429, 4923, 4927, 5421, 5425, 5943, 5947, 6489

Offset

1,1

Comments

See A277402 for illustrations.

Links

Lars Blomberg, Table of n, a(n) for n = 1..500

Formula

Empirically for 12 < n < 500: a(n) = a(n-2) + a(n-10) - a(n-12) + 120.

Conjectures from Colin Barker, Jun 08 2020: (Start)

G.f.: x*(3 + 4*x + 11*x^2 + 24*x^4 + 24*x^6 + 24*x^8 - 24*x^9 + 45*x^10 + 20*x^11 - 11*x^12) / ((1 - x)^3*(1 + x)^2*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-10) - a(n-11) - a(n-12) + a(n-13) for n>13.

(End)

Colin Barker's recurrence conjecture holds for 13 < n <= 500. Lars Blomberg, Jun 12 2020

Empirical: a(2*k - 1) = 3*(4*k^2 - 6*k + 3), for k >= 1. - Ivan N. Ianakiev, Jul 15 2020

Crossrefs

Cf. A331782, A277402 (regions), A335412 (edges), A335413 (ngons).

Sequence in context: A065496 A322922 A018479 * A331782 A090504 A018548

Adjacent sequences: A335408 A335409 A335410 * A335412 A335413 A335414

Keyword

nonn

Author

Lars Blomberg, Jun 08 2020

Status

approved