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 A132708 #31 Dec 12 2023 08:55:34 %S A132708 4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4, %T A132708 -2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4, %U A132708 2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1,4,2,1,-4,-2,-1 %N A132708 Period 6: repeat [4, 2, 1, -4, -2, -1]. %C A132708 Old definition was: "First differences of 5^n mod 9". %H A132708 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,-1). %F A132708 G.f.: (x^2 + 2*x + 4)/(x^3 + 1). - _Chai Wah Wu_, Jun 04 2016 %F A132708 From _Wesley Ivan Hurt_, Jun 28 2016: (Start) %F A132708 a(n) + a(n-3) = 0 for n>2. %F A132708 a(n) = a(n-6) for n>5. %F A132708 a(n) = cos(n*Pi) + 3*cos(n*Pi/3) + sqrt(3)*sin(n*Pi/3). (End) %p A132708 A132708:= n -> [4, 2, 1, -4, -2, -1][(n mod 6)+1]: seq(A132708(n), n=0..100); # _Wesley Ivan Hurt_, Jun 28 2016 %t A132708 PadRight[{}, 120, {4, 2, 1, -4, -2, -1}] (* _Harvey P. Dale_, Nov 21 2015 *) %t A132708 Differences[PowerMod[5, Range[0, 90], 9]] (* _Alonso del Arte_, Jun 04 2016 *) %o A132708 (Magma) &cat [[4,2,1,-4,-2,-1]^^30]; // _Wesley Ivan Hurt_, Jun 28 2016 %Y A132708 Cf. A070366 (5^n mod 9). %K A132708 sign,easy %O A132708 0,1 %A A132708 _Paul Curtz_, Nov 16 2007 %E A132708 Name changed by _Wesley Ivan Hurt_, Jun 28 2016