cp's OEIS Frontend

A110267 Total number of black cells at the first n generations of a single black cell following Wolfram's Rule 30 cellular automaton.

%I A110267 #27 Feb 16 2025 08:32:58
%S A110267 1,4,7,13,17,26,31,43,50,62,73,87,99,118,131,153,168,187,207,231,252,
%T A110267 275,298,326,352,379,405,438,468,502,533,572,598,637,666,712,744,788,
%U A110267 826,871,918,959,1004,1053,1091,1146,1188,1239,1283,1336,1379,1438,1490
%N A110267 Total number of black cells at the first n generations of a single black cell following Wolfram's Rule 30 cellular automaton.
%C A110267 At each generation, "looking back", one can see "behind", groups of black cells: total number of black cells (cumulative sum of first n terms of A070952).
%H A110267 Reinhard Zumkeller, <a href="/A110267/b110267.txt">Table of n, a(n) for n = 0..10000</a>
%H A110267 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30.</a>
%H A110267 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A110267 a(1)=1 because one black cell;
%e A110267 a(2)=4 because there are now 3 contiguous black cell connected to the first one, which form one only black surface of 4 cells;
%e A110267 a(3)=7 because appear three black cells: 4+3=7
%e A110267 From _Michael De Vlieger_, Dec 16 2015: (Start)
%e A110267 First 12 rows, replacing "0" with "." for better visibility of ON cells, followed by the total number of ON cells per row, and the running total up to that row:
%e A110267                 1                  =  1 ->   1
%e A110267               1 1 1                =  3 ->   4
%e A110267             1 1 . . 1              =  3 ->   7
%e A110267           1 1 . 1 1 1 1            =  6 ->  13
%e A110267         1 1 . . 1 . . . 1          =  4 ->  17
%e A110267       1 1 . 1 1 1 1 . 1 1 1        =  9 ->  26
%e A110267     1 1 . . 1 . . . . 1 . . 1      =  5 ->  31
%e A110267   1 1 . 1 1 1 1 . . 1 1 1 1 1 1    = 12 ->  43
%e A110267 1 1 . . 1 . . . 1 1 1 . . . . . 1  =  7 ->  50
%e A110267 (End)
%t A110267 Accumulate[Total /@ CellularAutomaton[30, {{1}, 0}, 52]] (* _Michael De Vlieger_, Dec 16 2015 *)
%o A110267 (Haskell)
%o A110267 a110267 n = a110267_list !! (n-1)
%o A110267 a110267_list = scanl1 (+) a070952_list
%o A110267 -- _Reinhard Zumkeller_, Jun 08 2013
%Y A110267 Cf. A070950, A051023, A092539, A092540, A070952, A100053, A100054, A100055, A094603, A094604, A000225, A074890.
%Y A110267 See A265704 for an essentially identical sequence.
%K A110267 easy,nonn
%O A110267 0,2
%A A110267 _Alexandre Wajnberg_, Sep 06 2005
%E A110267 Offset changed by _Reinhard Zumkeller_, Jun 08 2013