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 A059153 #69 Feb 16 2025 08:32:43
%S A059153 4,24,112,480,1984,8064,32512,130560,523264,2095104,8384512,33546240,
%T A059153 134201344,536838144,2147418112,8589803520,34359476224,137438429184,
%U A059153 549754765312,2199021158400,8796088827904,35184363700224,140737471578112,562949919866880
%N A059153 a(n) = 2^(n+2)*(2^(n+1)-1).
%C A059153 A hierarchical sequence (S(W'2{2}c) - see A059126).
%C A059153 a(n) written in base 2: 100, 11000, 1110000, ..., i.e., (n+1) times 1 and (n+2) times 0 (see A163663). - _Jaroslav Krizek_, Aug 12 2009
%C A059153 Also, the number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 513", based on the 5-celled von Neumann neighborhood. - _Robert Price_, May 04 2016
%D A059153 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A059153 Harry J. Smith, <a href="/A059153/b059153.txt">Table of n, a(n) for n = 0..200</a>
%H A059153 J. Wallgren, <a href="/A059126/a059126.txt">Hierarchical sequences</a>
%H A059153 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A059153 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A059153 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A059153 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A059153 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A059153 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8).
%F A059153 a(n) = A173787(2*n+3,n+2) = 4*A006516(n+1). - _Reinhard Zumkeller_, Feb 28 2010
%F A059153 From _Colin Barker_, Apr 28 2013: (Start)
%F A059153 a(n) = 6*a(n-1) - 8*a(n-2).
%F A059153 G.f.: 4 / ((2*x-1)*(4*x-1)). (End)
%F A059153 a(n) = 2*A020522(n+1). - _Hussam al-Homsi_, Jun 06 2021
%F A059153 E.g.f.: 4*exp(2*x)*(2*exp(2*x) - 1). - _Elmo R. Oliveira_, Dec 10 2023
%t A059153 Table[2^(n + 2)*(2^(n + 1) - 1), {n, 0, 23}] (* and *) LinearRecurrence[{6, -8}, {4, 24}, 40] (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2012 *)
%o A059153 (PARI) a(n) = { 2^(n + 2)*(2^(n + 1) - 1) } \\ _Harry J. Smith_, Jun 25 2009
%Y A059153 Cf. A006516, A020522, A059126, A163663, A173787, A272702.
%K A059153 easy,nonn
%O A059153 0,1
%A A059153 _Jonas Wallgren_, Feb 02 2001
%E A059153 Revised by _Henry Bottomley_, Jun 27 2005