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A110266 Number of blocks of ON cells in n-th row of triangle generated by Wolfram's "Rule 30".

%I A110266 #19 Feb 16 2025 08:32:58
%S A110266 1,1,2,2,3,3,4,3,4,5,6,6,7,7,8,7,7,8,10,9,9,11,14,12,11,12,15,16,14,
%T A110266 15,17,14,15,17,20,18,18,18,21,21,17,19,21,20,23,22,23,22,23,21,27,30,
%U A110266 26,27,29,29,28,28,33,31,30,31,36,32,28,29,33,33,33,35
%N A110266 Number of blocks of ON cells in n-th row of triangle generated by Wolfram's "Rule 30".
%C A110266 Old name was "Number of trees appearing at n-th generation of a black cell following Wolfram's Rule 30 cellular automaton."
%C A110266 At each generation, "looking back", one can see "behind", groups (sort of black isles) of contiguous black cells which after a while appear to be trees growing. It should be possible to describe each one of them in terms of trees theory.
%H A110266 Charlie Neder, <a href="/A110266/b110266.txt">Table of n, a(n) for n = 1..1000</a>
%H A110266 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30.</a>
%e A110266 a(1)=1 because one black cell;
%e A110266 a(2)=1 because there are now 3 contiguous black cell connected to the first one, which forms one only black surface;
%e A110266 a(3)=2 because two black cells are now connected to the preceding black surface and another black cell appears, which is isolated, so we have two separate black surfaces: 2.
%e A110266 From _Charlie Neder_, Feb 06 2019: (Start)
%e A110266 Rule 30 triangle begins:
%e A110266                      1
%e A110266                     111
%e A110266                    11  1
%e A110266                   11 1111
%e A110266                  11  1   1
%e A110266                 11 1111 111
%e A110266                11  1    1  1
%e A110266               11 1111  111111
%e A110266              11  1   111     1
%e A110266 and the number of blocks of ON cells in each row is 1, 1, 2, 2, 3, 3, 4, 3, 4, ... (End)
%Y A110266 Cf. A070950, A051023, A092539, A092540, A070952, A100053, A100054, A100055, A094603, A094604, A000225, A074890.
%K A110266 easy,nonn
%O A110266 1,3
%A A110266 _Alexandre Wajnberg_, Sep 06 2005
%E A110266 New name and a(17)-a(70) from _Charlie Neder_, Feb 06 2019