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 A134142 #20 May 19 2025 16:22:06
%S A134142 2,-3,2,2,-8,12,-8,-8,32,-48,32,32,-128,192,-128,-128,512,-768,512,
%T A134142 512,-2048,3072,-2048,-2048,8192,-12288,8192,8192,-32768,49152,-32768,
%U A134142 -32768,131072,-196608,131072,131072,-524288,786432,-524288,-524288,2097152,-3145728,2097152,2097152,-8388608
%N A134142 List of quadruples: 2*(-4)^n, -3*(-4)^n, 2*(-4^n), 2*(-4)^n, n >= 0.
%H A134142 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-2).
%F A134142 O.g.f.: (x+2)/(2*x^2+2*x+1). a(n) = 2*A108520(n)+A108520(n-1). - _R. J. Mathar_, Feb 05 2008
%F A134142 a(n) = (1 - I/2)*(-1 - I)^n + (1 + I/2)*(-1 + I)^n, n>=0. - _Taras Goy_, Apr 20 2019
%F A134142 a(n) = -2*a(n-1)-2*a(n-2) for n > 1. - _Chai Wah Wu_, May 19 2025
%F A134142 E.g.f.: exp(-x)*(2*cos(x) - sin(x)). - _Stefano Spezia_, May 19 2025
%p A134142 A134142 := proc(n) (-4)^floor(n/4)*op(1+(n mod 4), [2,-3,2,2]) ; end: for n from 0 to 80 do printf("%d ",A134142(n)) ; od: # _R. J. Mathar_, Feb 05 2008
%Y A134142 Cf. A081147, A038521.
%K A134142 tabf,easy,sign
%O A134142 0,1
%A A134142 _Paul Curtz_, Jan 29 2008
%E A134142 More terms from _R. J. Mathar_, Feb 05 2008