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 A080643 #24 Apr 03 2025 02:54:39
%S A080643 0,2,10,46,202,862,3610,14926,61162,249022,1009210,4076206,16422922,
%T A080643 66045982,265246810,1064175886,4266269482,17093775742,68461196410,
%U A080643 274103065966,1097187104842,4391072942302,17571265338010,70305982058446,281286690353002,1125335047769662
%N A080643 a(0)=0; for n>0, a(n) = 4^n - 2*3^(n-1).
%H A080643 Harvey P. Dale, <a href="/A080643/b080643.txt">Table of n, a(n) for n = 0..1000</a>
%H A080643 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-12).
%F A080643 G.f.: 2*x*(1-2*x)/((1-3*x)*(1-4*x)). - _Colin Barker_, Jan 20 2012
%F A080643 E.g.f.: (3*exp(4*x) - 2*exp(3*x) - 1)/3. - _Stefano Spezia_, Apr 03 2025
%t A080643 Join[{0},Table[4^n-2*3^(n-1),{n,30}]] (* or *) LinearRecurrence[{7,-12},{0,2,10},30] (* _Harvey P. Dale_, Dec 29 2023 *)
%o A080643 (Python)
%o A080643 def A080643(n): return (1<<(n<<1))-(3**(n-1)<<1) if n else 0 # _Chai Wah Wu_, Apr 02 2025
%Y A080643 Complement of A025192 in 4^n.
%K A080643 nonn,easy
%O A080643 0,2
%A A080643 _Max Alekseyev_, Feb 26 2003