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 A265431 #19 Feb 16 2025 08:33:27
%S A265431 0,1,4,7,12,18,26,34,44,55,68,81,96,112,130,148,168,189,212,235,260,
%T A265431 286,314,342,372,403,436,469,504,540,578,616,656,697,740,783,828,874,
%U A265431 922,970,1020,1071,1124,1177,1232,1288,1346,1404,1464,1525,1588,1651
%N A265431 Total number of OFF (white) cells after n iterations of the "Rule 188" elementary cellular automaton starting with a single ON (black) cell.
%D A265431 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A265431 Robert Price, <a href="/A265431/b265431.txt">Table of n, a(n) for n = 0..999</a>
%H A265431 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A265431 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A265431 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%F A265431 Conjectures from _Colin Barker_, Dec 09 2015 and Apr 16 2019: (Start)
%F A265431 a(n) = 1/16*(10*n^2+8*n+3*(-1)^n-2*(-i)^n-2*i^n+1) where i = sqrt(-1).
%F A265431 G.f.: x*(1+2*x+2*x^3) / ((1-x)^3*(1+x)*(1+x^2)).
%F A265431 (End)
%e A265431 From _Michael De Vlieger_, Dec 09 2015: (Start)
%e A265431 First 12 rows, replacing "1" with "." for better visibility of OFF cells,
%e A265431 followed by the total number of 0's per row, and the running total up to
%e A265431 that row:
%e A265431 . = 0 -> 0
%e A265431 . . 0 = 1 -> 1
%e A265431 . 0 . 0 0 = 3 -> 4
%e A265431 . . . . 0 0 0 = 3 -> 7
%e A265431 . . . 0 . 0 0 0 0 = 5 -> 12
%e A265431 . . 0 . . . 0 0 0 0 0 = 6 -> 18
%e A265431 . 0 . . . 0 . 0 0 0 0 0 0 = 8 -> 26
%e A265431 . . . . 0 . . . 0 0 0 0 0 0 0 = 8 -> 34
%e A265431 . . . 0 . . . 0 . 0 0 0 0 0 0 0 0 = 10 -> 44
%e A265431 . . 0 . . . 0 . . . 0 0 0 0 0 0 0 0 0 = 11 -> 55
%e A265431 . 0 . . . 0 . . . 0 . 0 0 0 0 0 0 0 0 0 0 = 13 -> 68
%e A265431 . . . . 0 . . . 0 . . . 0 0 0 0 0 0 0 0 0 0 0 = 13 -> 81
%e A265431 (End)
%t A265431 lim = 104; a = {}; Do[AppendTo[a, Take[#[[k]], 2 (k - 1) + 1]], {k, Floor[Length[#]/2]}] &@ CellularAutomaton[188, {{1}, 0}, lim]; Accumulate[Count[#, n_ /; n == 0] & /@ a] (* _Michael De Vlieger_, Dec 09 2015 *)
%Y A265431 Cf. A118174.
%K A265431 nonn,easy
%O A265431 0,3
%A A265431 _Robert Price_, Dec 08 2015