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.

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

(list; graph; refs; listen; history; text; internal format)

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 *)