A110267 - OEIS

A110267

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

%I #26 Jul 19 2021 01:18:20

%S 1,4,7,13,17,26,31,43,50,62,73,87,99,118,131,153,168,187,207,231,252,

%T 275,298,326,352,379,405,438,468,502,533,572,598,637,666,712,744,788,

%U 826,871,918,959,1004,1053,1091,1146,1188,1239,1283,1336,1379,1438,1490

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

%C 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 Reinhard Zumkeller, <a href="/A110267/b110267.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule30.html">Rule 30.</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%e a(1)=1 because one black cell;

%e 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 a(3)=7 because appear three black cells: 4+3=7

%e From _Michael De Vlieger_, Dec 16 2015: (Start)

%e 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 1 = 1 -> 1

%e 1 1 1 = 3 -> 4

%e 1 1 . . 1 = 3 -> 7

%e 1 1 . 1 1 1 1 = 6 -> 13

%e 1 1 . . 1 . . . 1 = 4 -> 17

%e 1 1 . 1 1 1 1 . 1 1 1 = 9 -> 26

%e 1 1 . . 1 . . . . 1 . . 1 = 5 -> 31

%e 1 1 . 1 1 1 1 . . 1 1 1 1 1 1 = 12 -> 43

%e 1 1 . . 1 . . . 1 1 1 . . . . . 1 = 7 -> 50

%e (End)

%t Accumulate[Total /@ CellularAutomaton[30, {{1}, 0}, 52]] (* _Michael De Vlieger_, Dec 16 2015 *)

%o (Haskell)

%o a110267 n = a110267_list !! (n-1)

%o a110267_list = scanl1 (+) a070952_list

%o -- _Reinhard Zumkeller_, Jun 08 2013

%Y Cf. A070950, A051023, A092539, A092540, A070952, A100053, A100054, A100055, A094603, A094604, A000225, A074890.

%Y See A265704 for an essentially identical sequence.

%K easy,nonn

%O 0,2

%A _Alexandre Wajnberg_, Sep 06 2005

%E Offset changed by _Reinhard Zumkeller_, Jun 08 2013