A335412 a(n) is the number of edges formed by n-secting the angles of an equilateral triangle.

3, 12, 39, 54, 123, 144, 255, 282, 435, 432, 663, 702, 939, 984, 1263, 1314, 1635, 1692, 2055, 2082, 2523, 2592, 3039, 3114, 3603, 3684, 4215, 4302, 4875, 4932, 5583, 5682, 6339, 6444, 7143, 7254, 7995, 8112, 8895, 8982, 9843, 9972, 10839, 10974, 11883, 12024

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) + 240.

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

G.f.: 3*x*(1 + 3*x + 8*x^2 + 2*x^3 + 14*x^4 + 2*x^5 + 14*x^6 + 2*x^7 + 14*x^8 - 10*x^9 + 25*x^10 + 11*x^11 - 6*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

Crossrefs

Cf. A332376, A277402 (regions), A335411 (vertices), A335413 (ngons).

Sequence in context: A350787 A222643 A129014 * A332376 A341712 A261384

Adjacent sequences: A335409 A335410 A335411 * A335413 A335414 A335415

Keyword

nonn

Author

Lars Blomberg, Jun 08 2020

Status

approved