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a(n) = 2*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=4.
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%I #20 Sep 08 2022 08:45:32

%S 1,4,6,4,-4,-16,-24,-16,16,64,96,64,-64,-256,-384,-256,256,1024,1536,

%T 1024,-1024,-4096,-6144,-4096,4096,16384,24576,16384,-16384,-65536,

%U -98304,-65536,65536,262144,393216,262144,-262144,-1048576,-1572864,-1048576,1048576

%N a(n) = 2*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=4.

%C Sequence opposite to its second differences.

%C Degenerate case of a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) with n > 3 (for which the sequence is identical to its fourth differences).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2).

%F G.f.: (1+2*x)/(1-2*x+2*x^2). - Colin Barker, Mar 28 2012

%F a(n) = (1/2 + 3*i/2)*(1 - i)^n + (1/2 - 3*i/2)*(1 + i)^n, n >= 0, where i=sqrt(-1). - _Taras Goy_, Apr 20 2019

%o (Magma) m:=41; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x)/(1-2*x+2*x^2))); // _Bruno Berselli_, Mar 28 2012

%K sign,easy

%O 0,2

%A _Paul Curtz_, Apr 18 2008

%E More terms from _Bruno Berselli_, Mar 28 2012