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 A072260 #19 Jun 20 2024 16:52:37
%S A072260 6,33,165,789,3669,16725,75093,333141,1463637,6378837,27612501,
%T A072260 118838613,508908885,2169853269,9216283989,39012619605,164640413013,
%U A072260 692921390421,2909124515157
%N A072260 a(n) = ((6*n+19)*4^n - 1)/3.
%C A072260 Related to Collatz function (for n>0). All terms are divisible by 3.
%H A072260 Harvey P. Dale, <a href="/A072260/b072260.txt">Table of n, a(n) for n = 0..1000</a>
%H A072260 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-24,16).
%F A072260 G.f.: 3*(2-7*x+4*x^2)/((1-x)*(1-4*x)^2). - _Bruno Berselli_, Dec 16 2011
%F A072260 E.g.f.: ((19 + 24*x)*exp(4*x) - exp(x))/3. - _G. C. Greubel_, Jan 14 2020
%p A072260 seq( ((6*n+19)*4^n -1)/3, n=0..20); # _G. C. Greubel_, Jan 14 2020
%t A072260 LinearRecurrence[{9,-24,16}, {6,33,165}, 20] (* _G. C. Greubel_, Jan 14 2020 *)
%t A072260 Table[((6n+19)4^n-1)/3,{n,0,20}] (* _Harvey P. Dale_, Jun 20 2024 *)
%o A072260 (PARI) a(n)=((6*n+19)*4^n-1)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A072260 (Magma) [((6*n+19)*4^n-1)/3: n in [0..20]]; // _G. C. Greubel_, Jan 14 2020
%o A072260 (Sage) [((6*n+19)*4^n-1)/3 for n in (0..20)] # _G. C. Greubel_, Jan 14 2020
%o A072260 (GAP) List([0..20], n-> ((6*n+19)*4^n-1)/3); # _G. C. Greubel_, Jan 14 2020
%Y A072260 Cf. A072257, A072258, A072259.
%K A072260 nonn,easy
%O A072260 0,1
%A A072260 N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
%E A072260 Edited and extended by _Henry Bottomley_, Aug 06 2002