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 A081631 #29 Aug 23 2024 22:04:17
%S A081631 1,6,4,24,16,96,64,384,256,1536,1024,6144,4096,24576,16384,98304,
%T A081631 65536,393216,262144,1572864,1048576,6291456,4194304,25165824,
%U A081631 16777216,100663296,67108864,402653184,268435456,1610612736,1073741824
%N A081631 a(n) = 2*2^n - (-2)^n.
%C A081631 Binomial transform of A081630. Inverse binomial transform of A081632.
%H A081631 Vincenzo Librandi, <a href="/A081631/b081631.txt">Table of n, a(n) for n = 0..1000</a>
%H A081631 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4).
%F A081631 G.f.: (1+6*x)/((1-2*x)*(1+2*x)).
%F A081631 E.g.f.: 2*exp(2*x)-exp(-2*x).
%t A081631 CoefficientList[Series[(1 + 6 x) / ((1 - 2 x) (1 + 2 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 10 2013 *)
%t A081631 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 A081631 (Magma) [2*2^n-(-2)^n: n in [0..40]]; // _Vincenzo Librandi_, Aug 10 2013
%o A081631 (PARI) a(n)=2*2^n-(-2)^n \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A081631 Cf. A081630, A081632.
%K A081631 nonn,easy
%O A081631 0,2
%A A081631 _Paul Barry_, Mar 26 2003