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 A153972 #35 Nov 11 2023 15:32:42
%S A153972 7,8,10,14,22,38,70,134,262,518,1030,2054,4102,8198,16390,32774,65542,
%T A153972 131078,262150,524294,1048582,2097158,4194310,8388614,16777222,
%U A153972 33554438,67108870,134217734,268435462,536870918,1073741830,2147483654
%N A153972 a(n) = 2^n + 6.
%C A153972 Old name was "a(n+1) = 2*(a(n) - 2) - 2, a(0) = 7".
%H A153972 Vincenzo Librandi, <a href="/A153972/b153972.txt">Table of n, a(n) for n = 0..1000</a>
%H A153972 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A153972 a(n+1) = A209724(2*n-1). - _L. Edson Jeffery_, Nov 28 2012
%F A153972 From _Vincenzo Librandi_, May 13 2014: (Start)
%F A153972 G.f.: (7 - 13*x)/((1 - x)*(1 - 2*x)).
%F A153972 a(n) = 2^n + 6.
%F A153972 a(n) = 3*a(n-1) - 2*a(n-2) for n > 1. (End)
%F A153972 E.g.f.: exp(2*x) + 6*exp(x). - _G. C. Greubel_, Sep 01 2016
%F A153972 a(n) = 2*a(n-1) - 6 with a(0) = 7. - _Elmo R. Oliveira_, Nov 11 2023
%t A153972 a=7; lst={a}; Do[a=(a-2)*2-2; AppendTo[lst,a], {n,30}]; lst
%t A153972 NestList[ 2# - 6 &, 7, 31] (* _Robert G. Wilson v_, Nov 28 2012 *)
%t A153972 CoefficientList[Series[(7 - 13 x)/((1 - x) (1 - 2 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, May 13 2014 *)
%t A153972 LinearRecurrence[{3,-2}, {7, 8}, 25] (* _G. C. Greubel_, Sep 01 2016 *)
%o A153972 (Magma) [2^n+6: n in [0..40]]; // _Vincenzo Librandi_, May 13 2014
%o A153972 (PARI) a(n)=2^n+6 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A153972 Cf. A209724.
%K A153972 nonn,easy
%O A153972 0,1
%A A153972 _Vladimir Joseph Stephan Orlovsky_, Jan 03 2009