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 A079319 #28 May 28 2024 15:11:17
%S A079319 1,3,9,29,101,373,1429,5589,22101,87893,350549,1400149,5596501,
%T A079319 22377813,89494869,357946709,1431721301,5726754133,22906754389,
%U A079319 91626493269,366504924501,1466017600853,5864066209109,23456256447829
%N A079319 a(0) = 1; for n >= 1, a(n) = 4*a(n-1) - (2^n-1).
%H A079319 Paolo Xausa, <a href="/A079319/b079319.txt">Table of n, a(n) for n = 0..1000</a>
%H A079319 David Singmaster, <a href="https://m500.org.uk/wp-content/uploads/2023/11/M195WEB.pdf">On the cellular automaton of Ulam and Warburton</a>, M500 Magazine of the Open University, #195 (December 2003), pp. 2-7. Also <a href="/A079314/a079314.pdf">cached copy</a>, included with permission.
%H A079319 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F A079319 a(n) = 2^n + (4^n-1)/3, n>=0.
%F A079319 a(n) = Sum_{i = 0..2^n - 1} A079314(i).
%F A079319 G.f.: (1-4x+2x^2)/((1-x)(1-2x)(1-4x)).
%t A079319 A079319list[nmax_]:=LinearRecurrence[{7,-14,8},{1,3,9},nmax+1];A079319list[50] (* _Paolo Xausa_, Jul 30 2023 *)
%o A079319 (PARI) a(n)=if(n<0,0,2^n+(4^n-1)/3)
%o A079319 (Python) A079319=lambda n: 2**n + 4**n//3 # _M. F. Hasler_, May 28 2024
%Y A079319 Cf. A079314, A079315, A079316, A079317, A079318.
%Y A079319 Records in A085194.
%K A079319 nonn,easy
%O A079319 0,2
%A A079319 _N. J. A. Sloane_, Feb 12 2003