This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335411 #17 Jul 16 2020 03:54:09 %S A335411 3,7,21,25,63,67,129,133,219,199,333,337,471,475,633,637,819,823,1029, %T A335411 1009,1263,1267,1521,1525,1803,1807,2109,2113,2439,2419,2793,2797, %U A335411 3171,3175,3573,3577,3999,4003,4449,4429,4923,4927,5421,5425,5943,5947,6489 %N A335411 a(n) is the number of vertices formed by n-secting the angles of an equilateral triangle. %C A335411 See A277402 for illustrations. %H A335411 Lars Blomberg, <a href="/A335411/b335411.txt">Table of n, a(n) for n = 1..500</a> %F A335411 Empirically for 12 < n < 500: a(n) = a(n-2) + a(n-10) - a(n-12) + 120. %F A335411 Conjectures from _Colin Barker_, Jun 08 2020: (Start) %F A335411 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)). %F A335411 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 A335411 (End) %F A335411 Colin Barker's recurrence conjecture holds for 13 < n <= 500. _Lars Blomberg_, Jun 12 2020 %F A335411 Empirical: a(2*k - 1) = 3*(4*k^2 - 6*k + 3), for k >= 1. - _Ivan N. Ianakiev_, Jul 15 2020 %Y A335411 Cf. A331782, A277402 (regions), A335412 (edges), A335413 (ngons). %K A335411 nonn %O A335411 1,1 %A A335411 _Lars Blomberg_, Jun 08 2020