A335412 - OEIS

%I #12 Jun 12 2020 08:42:13

%S 3,12,39,54,123,144,255,282,435,432,663,702,939,984,1263,1314,1635,

%T 1692,2055,2082,2523,2592,3039,3114,3603,3684,4215,4302,4875,4932,

%U 5583,5682,6339,6444,7143,7254,7995,8112,8895,8982,9843,9972,10839,10974,11883,12024

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

%C See A277402 for illustrations.

%H Lars Blomberg, <a href="/A335412/b335412.txt">Table of n, a(n) for n = 1..500</a>

%F Empirically for 12 < n < 500: a(n) = a(n-2) + a(n-10) - a(n-12) + 240.

%F Conjectures from _Colin Barker_, Jun 08 2020: (Start)

%F 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)).

%F 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.

%F (End)

%F Colin Barker's recurrence conjecture holds for 13 < n <= 500. _Lars Blomberg_, Jun 12 2020

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

%K nonn

%O 1,1

%A _Lars Blomberg_, Jun 08 2020