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 A080675 #37 Sep 08 2022 08:45:09
%S A080675 2,12,52,212,852,3412,13652,54612,218452,873812,3495252,13981012,
%T A080675 55924052,223696212,894784852,3579139412,14316557652,57266230612,
%U A080675 229064922452,916259689812,3665038759252,14660155037012,58640620148052,234562480592212,938249922368852
%N A080675 a(n) = (5*4^n - 8)/6.
%C A080675 These numbers have a simple binary pattern: 10,1100,110100,11010100,1101010100, ... i.e., the n-th term has a binary expansion 1(10){n-1}0, that is, there are n-1 10's between the most significant 1 and the least significant 0.
%H A080675 Vincenzo Librandi, <a href="/A080675/b080675.txt">Table of n, a(n) for n = 1..170</a>
%H A080675 Andrei Asinowski, Cyril Banderier, Benjamin Hackl, <a href="https://www.semanticscholar.org/paper/On-extremal-cases-of-pop-stack-sorting-Asinowski/4b17b76c31559d6d8126b8f1126fdb357f3a5df0">On extremal cases of pop-stack sorting</a>, Permutation Patterns (Zürich, Switzerland, 2019).
%H A080675 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F A080675 a(1)=2, a(2)=12, a(n)=5*a(n-1)-4*a(n-2). - _Harvey P. Dale_, Oct 16 2012
%t A080675 (5*4^Range[30]-8)/6 (* or *) LinearRecurrence[{5,-4},{2,12},30] (* _Harvey P. Dale_, Oct 16 2012 *)
%o A080675 (Magma) [(5*4^n-8)/6: n in [1..40] ]; // _Vincenzo Librandi_, Apr 28 2011
%o A080675 (PARI) a(n)=(5*4^n-8)/6 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A080675 a(n) = A072197(n-1) - 1 = A014486(|A106191(n)|). a(n) = A079946(A020988(n-2)) for n>=2. Cf. also A122229.
%K A080675 nonn,easy
%O A080675 1,1
%A A080675 _N. J. A. Sloane_, Mar 02 2003
%E A080675 Further comments added by _Antti Karttunen_, Sep 14 2006