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
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
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
Comments