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 A189442 #18 May 08 2021 10:52:51 %S A189442 1,3,1,-3,-5,-7,-1,7,9,11,1,-11,-13,-15,-1,15,17,19,1,-19,-21,-23,-1, %T A189442 23,25,27,1,-27,-29,-31,-1,31,33,35,1,-35,-37,-39,-1,39,41,43,1,-43, %U A189442 -45,-47,-1,47,49,51,1,-51,-53,-55,-1,55,57,59,1,-59,-61,-63,-1,63 %N A189442 a(n) = A140230(n) / A016116(n-1). %C A189442 If grouped into blocks of four, %C A189442 1, 3, 1, -3, %C A189442 -5, -7, -1, 7, %C A189442 9, 11, 1, -11, %C A189442 -13, -15, -1, 15 %C A189442 17, 19, 1, -19. %C A189442 we see that a(4n+1) + a(4n+2) + a(4n+3) + a(4n+4) = (-1)^n*(2+4*n). %H A189442 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,-2,0,0,0,-1). %F A189442 a(n) = -2*a(n-4) - a(n-8). a(n) + a(n-4) = period length 8: repeat -4, -4, 0, 4, 4, 4, 0 -4. %F A189442 G.f. x*(x-1)*(x^4-2*x-1)*(1+x)^2 / (x^4+1)^2. - _R. J. Mathar_, Jun 02 2011 %F A189442 a(n) = (-1)^floor(n/4)*(1+3*n+(n-1)*(-1)^n-4*cos(n*Pi/2)+2*(n-1)*sin(n*Pi/2) )/4. - _Wesley Ivan Hurt_, May 08 2021 %o A189442 (PARI) Vec(x*(x-1)*(x^4-2*x-1)*(1+x)^2 / (x^4+1)^2+O(x^99)) \\ _Charles R Greathouse IV_, Jun 08 2011 %K A189442 sign,easy %O A189442 1,2 %A A189442 _Paul Curtz_, Apr 22 2011 %E A189442 More terms from _Jinyuan Wang_, Feb 26 2020