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

1, 4, 7, 13, 17, 26, 31, 43, 50, 62, 73, 87, 99, 118, 131, 153, 168, 187, 207, 231, 252, 275, 298, 326, 352, 379, 405, 438, 468, 502, 533, 572, 598, 637, 666, 712, 744, 788, 826, 871, 918, 959, 1004, 1053, 1091, 1146, 1188, 1239, 1283, 1336, 1379, 1438, 1490

Offset: 0

Author

Alexandre Wajnberg, Sep 06 2005

Keywords

• easy
• nonn

Comments

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).

Examples

			a(1)=1 because one black cell;
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;
a(3)=7 because appear three black cells: 4+3=7
From _Michael De Vlieger_, Dec 16 2015: (Start)
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:
                1                  =  1 ->   1
              1 1 1                =  3 ->   4
            1 1 . . 1              =  3 ->   7
          1 1 . 1 1 1 1            =  6 ->  13
        1 1 . . 1 . . . 1          =  4 ->  17
      1 1 . 1 1 1 1 . 1 1 1        =  9 ->  26
    1 1 . . 1 . . . . 1 . . 1      =  5 ->  31
  1 1 . 1 1 1 1 . . 1 1 1 1 1 1    = 12 ->  43
1 1 . . 1 . . . 1 1 1 . . . . . 1  =  7 ->  50
(End)
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Rule 30.
• Index entries for sequences related to cellular automata

Crossrefs

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

See A265704 for an essentially identical sequence.

Programs

Haskell

a110267 n = a110267_list !! (n-1)
a110267_list = scanl1 (+) a070952_list
-- Reinhard Zumkeller, Jun 08 2013

Mathematica

Accumulate[Total /@ CellularAutomaton[30, {{1}, 0}, 52]] (* Michael De Vlieger, Dec 16 2015 *)

Extensions

Offset changed by Reinhard Zumkeller, Jun 08 2013