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 A266176 #38 Feb 16 2025 08:33:28
%S A266176 1,2,4,107,16,1967,64,32447,256,523007,1024,8383487,4096,134197247,
%T A266176 16384,2147401727,65536,34359410687,262144,549754503167,1048576,
%U A266176 8796087779327,4194304,140737467383807,16777216,2251799729799167,67108864,36028796683419647,268435456
%N A266176 Decimal representation of the n-th iteration of the "Rule 5" elementary cellular automaton starting with a single ON (black) cell.
%D A266176 Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A266176 Robert Price, <a href="/A266176/b266176.txt">Table of n, a(n) for n = 0..999</a>
%H A266176 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A266176 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A266176 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A266176 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,21,0,-84,0,64).
%F A266176 From _Colin Barker_, Dec 23 2015 and Apr 13 2019: (Start)
%F A266176 a(n) = 21*a(n-2) - 84*a(n-4) + 64*a(n-6) for n>5.
%F A266176 G.f.: (1+2*x-17*x^2+65*x^3+16*x^4-112*x^5) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)*(1-4*x)*(1+4*x)).
%F A266176 (End)
%F A266176 a(n) = 2^n = A000079(n) for even n>=0; a(n) = 2*4^n - 5*2^(n-1) - 1 = A188530(n) for odd n. - _Karl V. Keller, Jr._, Jun 19 2021
%t A266176 rule = 5; rows = 30; Table[FromDigits[Table[Take[CellularAutomaton[rule,{{1},0}, rows-1, {All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]],2], {k,1,rows}]
%o A266176 (Python) print([2*4**n -5*2**(n-1) -1 if n%2 else 2**n for n in range(30)]) # _Karl V. Keller, Jr._, Jun 20 2021
%Y A266176 Cf. A266174, A266175, A000079, A188530.
%K A266176 nonn,easy
%O A266176 0,2
%A A266176 _Robert Price_, Dec 22 2015