%I #21 Sep 08 2022 08:45:09
%S 1,6,4,24,16,96,64,384,256,1536,1024,6144,4096,24576,16384,98304,
%T 65536,393216,262144,1572864,1048576,6291456,4194304,25165824,
%U 16777216,100663296,67108864,402653184,268435456,1610612736,1073741824
%N 2*2^n-(-2)^n.
%C Binomial transform of A081630. Inverse binomial transform of A081632.
%H Vincenzo Librandi, <a href="/A081631/b081631.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,4)
%F G.f.: (1+6*x)/((1-2*x)*(1+2*x)).
%F E.g.f. 2*exp(2*x)-exp(-2*x).
%t CoefficientList[Series[(1 + 6 x) / ((1 - 2 x) (1 + 2 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 10 2013 *)
%t LinearRecurrence[{0,4},{1,6},40] (* or *) With[{nn=20},Riffle[ NestList[ 4#&,1,nn],NestList[4#&,6,nn]]] (* _Harvey P. Dale_, Aug 04 2019 *)
%o (Magma) [2*2^n-(-2)^n: n in [0..40]]; // _Vincenzo Librandi_, Aug 10 2013 *)
%o (PARI) a(n)=2*2^n-(-2)^n \\ _Charles R Greathouse IV_, Oct 07 2015
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 26 2003
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