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 A168244 #49 Sep 08 2022 08:45:48
%S A168244 1,2,-1,-8,-19,-34,-53,-76,-103,-134,-169,-208,-251,-298,-349,-404,
%T A168244 -463,-526,-593,-664,-739,-818,-901,-988,-1079,-1174,-1273,-1376,
%U A168244 -1483,-1594,-1709,-1828,-1951,-2078,-2209,-2344,-2483,-2626,-2773,-2924,-3079,-3238,-3401,-3568,-3739,-3914,-4093,-4276,-4463,-4654,-4849
%N A168244 a(n) = 1 + 3*n - 2*n^2.
%C A168244 Consider the quadratic cyclotomic polynomial f(x) = x^2+x+1 and the quotients f(x + n*f(x))/f(x), as in A168235 and A168240. a(n) is the real part of the quotient at x = 1+sqrt(-5).
%C A168244 The imaginary part of the quotient is sqrt(5)*A045944(n).
%C A168244 As stated in short description of A168244 the quotient is in two parts: rational integers (cf. A168244) and rational integer multiples of sqrt(-5). It so happens that the sequence of rational integer coefficients of sqrt(-5) is A045944. - _A.K. Devaraj_, Nov 22 2009
%C A168244 This sequence contains half of all integers m such that -8*m +17 is an odd square. The other half are found in A091823 multiplied by -1. The squares resulting from A168244 are (4*n - 3)^2, those from A091823 are (4*n + 3)^2. - _Klaus Purath_, Jul 11 2021
%H A168244 Vincenzo Librandi, <a href="/A168244/b168244.txt">Table of n, a(n) for n = 0..1000</a>
%H A168244 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A168244 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A168244 G.f.: 1 + x*(2-7*x+x^2)/(1-x)^3.
%F A168244 a(-n) = -A091823(n), a(0) = 1. - _Michael Somos_, May 11 2014
%F A168244 E.g.f.: (1 + x - 2*x^2)*exp(x). - _G. C. Greubel_, Apr 09 2016
%F A168244 a(n) = a(n-2) + (-2)*sqrt((-8)*a(n-1) + 17), n > 1. - _Klaus Purath_, Jul 08 2021
%t A168244 Table[-(n + (n + 1)^2 - 3)/2, {n, -1, 200, 2}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 26 2011 *)
%t A168244 LinearRecurrence[{3,-3,1},{2,-1,-8},60] (* _Harvey P. Dale_, Jun 06 2015 *)
%o A168244 (Magma) [1+3*n-2*n^2: n in [1..50]]; // _Vincenzo Librandi_, Jul 10 2012
%o A168244 (PARI) a(n) = 1 + 3*n - 2*n^2; \\ _Altug Alkan_, Apr 09 2016
%Y A168244 Cf. A168235, A168240, A165806, A165808, A165809, A045944, A091823.
%K A168244 sign,easy
%O A168244 0,2
%A A168244 _A.K. Devaraj_, Nov 21 2009
%E A168244 Edited, definition simplified, sequence extended beyond a(5) by _R. J. Mathar_, Nov 23 2009
%E A168244 a(0)=1 added by _N. J. A. Sloane_, Apr 09 2016