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 A072262 #30 Sep 08 2022 08:45:06
%S A072262 11,45,181,725,2901,11605,46421,185685,742741,2970965,11883861,
%T A072262 47535445,190141781,760567125,3042268501,12169074005,48676296021,
%U A072262 194705184085,778820736341,3115282945365,12461131781461,49844527125845
%N A072262 a(n) = 4*a(n-1) + 1, a(1)=11.
%C A072262 These are the integers N which on application of the Collatz function yield the number 17. The Collatz function: if N is an odd number then (3N+1)/2^r yields a positive odd integer for some value of r (which in this case is 17).
%C A072262 Numbers whose binary representation is 1011 together with n - 1 times 01. For example, a(4) = 725 = 1011010101 (2). - _Omar E. Pol_, Nov 24 2012
%H A072262 G. C. Greubel, <a href="/A072262/b072262.txt">Table of n, a(n) for n = 1..1000</a>
%H A072262 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%H A072262 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A072262 From _Bruno Berselli_, Dec 16 2011: (Start)
%F A072262 G.f.: x*(11-10*x)/(1-5*x+4*x^2).
%F A072262 a(n) = (17*2^(2*n-1) - 1)/3.
%F A072262 Sum_{i=1..n} a(i) = (a(n+1) - n + 1)/3 - 4. (End)
%F A072262 a(n) = 34*A002450(n-1) + 11 . - _Yosu Yurramendi_, Jan 24 2017
%F A072262 E.g.f.: (-15 - 2*exp(x) + 17*exp(4*x))/6. - _G. C. Greubel_, Jan 14 2020
%F A072262 a(n) = A178415(6, n) = A347834(5, n-1), arrays, for n >= 1. - _Wolfdieter Lang_, Nov 29 2021
%p A072262 seq( (17*4^n -2)/6, n=1..30); # _G. C. Greubel_, Jan 14 2020
%t A072262 a[n_]:= 4a[n-1] +1; a[1]=11; Table[a[n], {n,25}]
%t A072262 NestList[4#+1&,11,30] (* or *) LinearRecurrence[{5,-4},{11,45},30] (* _Harvey P. Dale_, Dec 25 2014 *)
%o A072262 (PARI) vector(30, n, (17*4^n -2)/6) \\ _G. C. Greubel_, Jan 14 2020
%o A072262 (Magma) [(17*4^n -2)/6: n in [1..30]]; // _G. C. Greubel_, Jan 14 2020
%o A072262 (Sage) [(17*4^n -2)/6 for n in (1..30)] # _G. C. Greubel_, Jan 14 2020
%o A072262 (GAP) List([1..30], n-> (17*4^n -2)/6); # _G. C. Greubel_, Jan 14 2020
%Y A072262 Cf. A072257, A072258, A072259, A072260, A072261, A099730, A178415, A347834.
%K A072262 nonn,easy
%O A072262 1,1
%A A072262 N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
%E A072262 Edited and extended by _Robert G. Wilson v_, Jul 17 2002