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 A153265 #20 Mar 17 2024 12:54:54
%S A153265 4,1,-9,-2,31,1,-126,1,511,-2,-2049,1,8194,1,-32769,-2,131071,1,
%T A153265 -524286,1,2097151,-2,-8388609,1,33554434,1,-134217729,-2,536870911,1,
%U A153265 -2147483646,1,8589934591,-2,-34359738369,1
%N A153265 a(n) = (-2*I)^n + (2*I)^n + (1/2 + 1/2*I*sqrt(3))^n + (1/2 - 1/2*I*sqrt(3))^n.
%C A153265 For all n there is an m such that: ||a(n)| - 2^m| <= 2. In the Python program which will be provided, the sequence (a(n)) is given by 4tesseq(X) where X = 1.5'i + .25(ii + jj + kk + ee) is the generating floretion.
%H A153265 Vincenzo Librandi, <a href="/A153265/b153265.txt">Table of n, a(n) for n = 0..1000</a>
%H A153265 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,-5,4,-4).
%F A153265 a(n) = a(n-1) - 5a(n-2) + 4a(n-3) - 4a(n-4).
%F A153265 G.f.: 4 + x*(1-10*x+12*x^2-16*x^3)/((x^2-x+1)*(4*x^2+1)). - corrected by _Vaclav Kotesovec_, Jun 25 2014
%e A153265 a(4) = 32 + (1/2 + 1/2*I*sqrt(3))^4 + (1/2 - 1/2*I*sqrt(3))^4 = 31 -or- a(4) = a(n-1) - 5a(n-2) + 4a(n-3) - 4a(n-4) = -2 - 5*(-9) + 4*(1) - 4*4 = 31
%p A153265 a := n-> (2*I)^n+(-2*I)^n+(1/2+1/2*I*sqrt(3))^n+(1/2-1/2*I*sqrt(3))^n;
%t A153265 CoefficientList[Series[4 + x (1 - 10 x + 12 x^2 - 16 x^3)/((x^2 - x + 1) (4 x^2 + 1)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 26 2014 *)
%o A153265 (PARI) a(n)=2*(n%2<1)*(-4)^(n\2)+3*(n%3<1)*(-1)^(n\3)-(-1)^n \\ _Tani Akinari_, Jun 25 2014
%o A153265 (Magma) I:=[4,1,-9,-2]; [n le 4 select I[n] else Self(n-1)-5*Self(n-2)+4*Self(n-3) -4*Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Jun 26 2014
%Y A153265 Cf. A153266, A153267, A153268.
%K A153265 easy,sign
%O A153265 0,1
%A A153265 _Creighton Dement_, Dec 22 2008, Dec 31 2008