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

0,2

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).

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

Example

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)

Mathematica

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

Prog

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

Crossrefs

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

See A265704 for an essentially identical sequence.

Sequence in context: A310821 A310822 A265704 * A049698 A288823 A310823

Adjacent sequences: A110264 A110265 A110266 * A110268 A110269 A110270

Keyword

easy,nonn

Author

Alexandre Wajnberg, Sep 06 2005

Extensions

Offset changed by Reinhard Zumkeller, Jun 08 2013

Status

approved