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%I #21 Sep 08 2022 08:45:48
%S -1,6,-4,0,-16,-24,-64,-120,-256,-504,-1024,-2040,-4096,-8184,-16384,
%T -32760,-65536,-131064,-262144,-524280,-1048576,-2097144,-4194304,
%U -8388600,-16777216,-33554424,-67108864,-134217720,-268435456,-536870904,-1073741824,-2147483640
%N a(n) = 4*( 1-(-1)^n) -2^n.
%H Vincenzo Librandi, <a href="/A166978/b166978.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F a(n) = A166956(n+1)-3*A166956(n).
%F a(2n) = -A000302(n). a(2n+1) = 6*(-1)^n*A084240(n).
%F a(n+1) - 2*a(n) = 4*( 3*(-1)^n-1) = 8 *(-1)^n*A000034(n).
%F G.f.: -(5*x-1)*(3*x-1) / ( (x-1)*(2*x-1)*(1+x) ). - _R. J. Mathar_, Jul 01 2011
%F E.g.f.: 8*sinh(x) - exp(2*x). - _G. C. Greubel_, May 30 2016
%t LinearRecurrence[{2,1,-2}, {-1, 6, -4}, 50] (* or *) Table[4*(1-(-1)^n) - 2^n, {n,0,25}] (* _G. C. Greubel_, May 30 2016 *)
%o (Magma) [4*( 1-(-1)^n) -2^n: n in [0..40] ]; // _Vincenzo Librandi_, Aug 06 2011
%K easy,sign
%O 0,2
%A _Paul Curtz_, Oct 26 2009