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 A072261 #34 Sep 04 2023 11:26:24
%S A072261 7,29,117,469,1877,7509,30037,120149,480597,1922389,7689557,30758229,
%T A072261 123032917,492131669,1968526677,7874106709,31496426837,125985707349,
%U A072261 503942829397,2015771317589,8063085270357,32252341081429,129009364325717,516037457302869
%N A072261 a(n) = 4*a(n-1) + 1, a(1)=7.
%C A072261 These are the integers N which on application of the Collatz function yield the number 11. 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 11).
%C A072261 These numbers reach 11 in Collatz function iteration after 2(n+1) steps and so end in 1 after exactly 2n+18 steps. - Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 08 2004
%C A072261 Numbers whose binary representation is 111 together with n - 1 times 01. For example, a(4) = 469 = 111010101 (2). - _Omar E. Pol_, Nov 24 2012
%H A072261 Colin Barker, <a href="/A072261/b072261.txt">Table of n, a(n) for n = 1..1000</a>
%H A072261 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%H A072261 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A072261 a(n) = (11*4^n - 2)/6 = 22*A002450(n-1) + 7. - Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 08 2004
%F A072261 From _Colin Barker_, Oct 27 2019: (Start)
%F A072261 G.f.: x*(7 - 6*x) / ((1 - x)*(1 - 4*x)).
%F A072261 a(n) = 5*a(n-1) - 4*a(n-2) for n>2. (End)
%F A072261 E.g.f.: (-9 - 2*exp(x) + 11*exp(4*x))/6. - _G. C. Greubel_, Jan 14 2020
%F A072261 a(n) = a(n-1) + 11*2^(2*n-3), for n >= 2, with a(1) = 7. - _Wolfdieter Lang_, Aug 16 2021
%F A072261 a(n) = A178415(4, n) = A347834(3, n-1), arrays, for n >= 1. - _Wolfdieter Lang_, Nov 29 2021
%p A072261 seq(coeff(series(x*(7-6*x)/((1-x)*(1-4*x)), x, n+1), x, n), n = 1..25); # _G. C. Greubel_, Jan 14 2020
%t A072261 a[n_]:= 4a[n-1] +1; a[1]=7; Table[a[n], {n,25}]
%t A072261 NestList[4#+1&,7,30] (* or *) LinearRecurrence[{5,-4},{7,29},30] (* _Harvey P. Dale_, Sep 04 2023 *)
%o A072261 (PARI) Vec(x*(7-6*x)/((1-x)*(1-4*x)) + O(x^25)) \\ _Colin Barker_, Oct 27 2019
%o A072261 (Magma) [(11*4^n -2)/6: n in [1..25]]; // _G. C. Greubel_, Jan 14 2020
%o A072261 (Sage) [(11*4^n -2)/6 for n in (1..25)] # _G. C. Greubel_, Jan 14 2020
%o A072261 (GAP) List([1..25], n-> (11*4^n -2)/6); # _G. C. Greubel_, Jan 14 2020
%Y A072261 Cf. A002450, A072197, A072257, A072258, A072259, A072260, A072262, A099730, A178415, A347834.
%K A072261 nonn,easy
%O A072261 1,1
%A A072261 N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
%E A072261 Edited and extended by _Robert G. Wilson v_, Jul 17 2002
%E A072261 More terms from _Colin Barker_, Oct 27 2019