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 A077966 #36 Sep 08 2022 08:45:08
%S A077966 1,0,-2,0,4,0,-8,0,16,0,-32,0,64,0,-128,0,256,0,-512,0,1024,0,-2048,0,
%T A077966 4096,0,-8192,0,16384,0,-32768,0,65536,0,-131072,0,262144,0,-524288,0,
%U A077966 1048576,0,-2097152,0,4194304,0,-8388608,0,16777216,0,-33554432,0,67108864,0,-134217728,0,268435456
%N A077966 Expansion of 1/(1+2*x^2).
%C A077966 Normally sequences like this are not included, since with the alternating 0's deleted it is already in the database.
%C A077966 Inverse binomial transform of A087455. - _Philippe Deléham_, Dec 02 2008
%C A077966 Pisano period lengths: 1, 1, 2, 1, 8, 2, 12, 1, 6, 8, 10, 2, 24, 12, 8, 1, 16, 6, 18, 8,... - _R. J. Mathar_, Aug 10 2012
%H A077966 G. C. Greubel, <a href="/A077966/b077966.txt">Table of n, a(n) for n = 0..1000</a>
%H A077966 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,-2).
%F A077966 a(n) = (1+(-1)^n)*(-2)^(n/2)/2. - _R. J. Mathar_, Apr 23 2009
%F A077966 a(n) = ((n+1) mod 2 )*(-2)^floor((n+1)/2). - _Wesley Ivan Hurt_, Apr 06 2014
%F A077966 E.g.f.: cos(sqrt(2)*x). - _G. C. Greubel_, Jun 24 2019
%p A077966 A077966:=n->(1+(-1)^n)*(-2)^(n/2)/2; seq(A077966(n), n=0..50); # _Wesley Ivan Hurt_, Apr 02 2014
%t A077966 CoefficientList[Series[1/(1 + 2*x^2), {x,0,60}], x] (* _Vladimir Joseph Stephan Orlovsky_, Jun 10 2011 *)
%t A077966 LinearRecurrence[{0,-2}, {1,0}, 60] (* _G. C. Greubel_, Jun 24 2019 *)
%o A077966 (Sage) [lucas_number1(n,0,2) for n in range(1,60)] # _Zerinvary Lajos_, Jul 16 2008
%o A077966 (PARI) Vec(1/(1+2*x^2)+O(x^60)) \\ _Charles R Greathouse IV_, Sep 24 2012
%o A077966 (PARI) for(n=0, 51, print1(imag(quadgen(-8)^(n+1)), ", ")) \\ _Arkadiusz Wesolowski_, Dec 26 2012
%o A077966 (Magma) I:=[1,0]; [n le 2 select I[n] else -2*Self(n-2): n in [1..60]]; // _G. C. Greubel_, Jun 24 2019
%o A077966 (GAP) a:=[1,0];; for n in [3..60] do a[n]:=-2*a[n-2]; od; a; # _G. C. Greubel_, Jun 24 2019
%Y A077966 Cf. A000079, A077957.
%K A077966 sign,easy
%O A077966 0,3
%A A077966 _N. J. A. Sloane_, Nov 17 2002