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 A179415 #11 Nov 27 2019 11:14:47 %S A179415 6,6,6,8,10,12,16,18,20,26,24,28,30,22,32,28,32,36,48,42,56,34,26,28, %T A179415 40,38,50,48,46,64,48,46,48,46,48,56,52,66,62,66,68,86,60,70,64,72,50, %U A179415 50,50,40,42,46,48,36,38,36,42,48,46,44,34,30,26,22,20,16,16,16,16,16 %N A179415 The number of alive cells in Conway's Game of Life on the infinite square grid, in the "lumps of muck" sequence of patterns leading from the grandfather of "stairstep hexomino" to a stable configuration of four blocks, known as a blockade. %C A179415 For n >= 65, a(n)=16. Note that the same history is traced on any toroidal grid with size at least 26 X 26. %C A179415 All terms are even because the initial pattern has an even number of cells and because it has 180-degree rotational symmetry. %H A179415 Antti Karttunen, <a href="/A179409/a179409.ijs.txt">J-program for computing the terms of this sequence</a> %H A179415 Stephen A. Silver, <a href="https://conwaylife.com/ref/lexicon/lex_l.htm#lumpsofmuck">Life Lexicon, "lumps of muck"</a> %e A179415 The generations 0-3 of this cycle of patterns look as follows, thus a(0)=a(1)=a(2)=6 and a(3)=8. %e A179415 . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . %e A179415 . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . %e A179415 . . o . . . . . | . . . . . . . . | . . o . . . . . | . . o o . . . . %e A179415 . o . . o . . . | . o o o . . . . | . . o o . . . . | . . o . o . . . %e A179415 . . o . . o . . | . . . o o o . . | . . . o o . . . | . . o . o . . . %e A179415 . . . . o . . . | . . . . . . . . | . . . . o . . . | . . . o o . . . %e A179415 . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . %e A179415 . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . %e A179415 ..................................|stairstep hexomino................ %e A179415 Generations 4-7 of this cycle of patterns look as follows, thus a(4)=10, a(5)=12, a(6)=16 and a(7)=18. %e A179415 . . . . . . . . | . . . . . . . . | . . . . . . . . | . . . . . . . . %e A179415 . . . . . . . . | . . . . . . . . | . . o . . . . . | . o o . . . . . %e A179415 . . o o . . . . | . o o o . . . . | . o o o o . . . | . o o . o o . . %e A179415 . o o . o . . . | . o . . o o . . | o . . . o o . . | o . . . o o . . %e A179415 . . o . o o . . | . o o . . o . . | . o o . . . o . | . o o . . . o . %e A179415 . . . o o . . . | . . . o o o . . | . . o o o o . . | . o o . o o . . %e A179415 . . . . . . . . | . . . . . . . . | . . . . o . . . | . . . . o o . . %e A179415 .(handshake). . | . . . . . . . . | . . . . . . . . | . . . . . . . . %e A179415 At generation 65, the following stable formation of four blocks is reached, called "blockade", and thus for n >= 65, a(n)=16. %e A179415 o o . . . . . . . . . . . . . . . . . . . . . %e A179415 o o . . . . . . . . . . . . . . . . . . . . . %e A179415 . . . . . . . . . . . . . . . . . . . . . . . %e A179415 . . . . . . . . . . . . . . . . . . . . . . . %e A179415 . o o . . . . . . . . . . . . . . . . . o o . %e A179415 . o o . . . . . . . . . . . . . . . . . o o . %e A179415 . . . . . . . . . . . . . . . . . . . . . . . %e A179415 . . . . . . . . . . . . . . . . . . . . . . . %e A179415 . . . . . . . . . . . . . . . . . . . . . o o %e A179415 . . . . . . . . . . . . . . . . . . . . . o o %Y A179415 A179409, which traces the history of the same initial pattern on an 8 X 8 toroidal grid, differs from this one for the first time at n=14, as a(14)=32, while A179409(14)=26. %K A179415 nonn %O A179415 0,1 %A A179415 _Antti Karttunen_, Jul 27 2010