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 A146306 #20 May 08 2025 14:32:09
%S A146306 -5,-1,-1,-1,-1,0,1,1,1,1,5,1,7,2,3,5,11,1,13,7,5,4,17,3,19,5,7,11,23,
%T A146306 2,25,13,9,7,29,5,31,8,11,17,35,3,37,19,13,10,41,7,43,11,15,23,47,4,
%U A146306 49,25,17,13,53,9,55,14,19,29,59,5,61,31,21,16,65,11,67,17,23,35,71,6,73,37
%N A146306 a(n) = numerator of (n-6)/(2n).
%C A146306 For denominators see A146307.
%C A146306 General formula:
%C A146306 2*cos(2*Pi/n) = Hypergeometric2F1((n-6)/(2n), (n+6)/(2n), 1/2, 3/4) =
%C A146306 Hypergeometric2F1(a(n)/A146307(n), a(n+12)/A146307(n), 1/2, 3/4).
%C A146306 2*cos(2*Pi/n) is root of polynomial of degree = EulerPhi(n)/2 = A000010(n)/2 = A023022(n).
%C A146306 Records in this sequence are congruent to 1 or 5 mod 6 (see A007310).
%C A146306 First occurrence n in this sequence see A146308.
%H A146306 <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,-1).
%F A146306 a(n+5) = A051724(n).
%F A146306 Sum_{k=1..n} a(k) ~ (77/288) * n^2. - _Amiram Eldar_, Apr 04 2024
%F A146306 From _Chai Wah Wu_, May 08 2025: (Start)
%F A146306 a(n) = 2*a(n-12) - a(n-24) for n > 24.
%F A146306 G.f.: x*(x^23 + 7*x^22 + 2*x^21 + 3*x^20 + 5*x^19 + 11*x^18 + x^17 + 13*x^16 + 7*x^15 + 5*x^14 + 4*x^13 + 17*x^12 + x^11 + 5*x^10 + x^9 + x^8 + x^7 + x^6 - x^4 - x^3 - x^2 - x - 5)/(x^24 - 2*x^12 + 1). (End)
%e A146306 Fractions begin with -5/2, -1, -1/2, -1/4, -1/10, 0, 1/14, 1/8, 1/6, 1/5, 5/22, 1/4, ...
%t A146306 Table[Numerator[(n - 6)/(2 n)], {n, 1, 100}]
%Y A146306 Cf. A000010, A007310, A023022, A051724, A146307 (denominators), A146308.
%K A146306 sign,easy
%O A146306 1,1
%A A146306 _Artur Jasinski_, Oct 29 2008