A265223 Total number of OFF (white) cells after n iterations of the "Rule 150" elementary cellular automaton starting with a single ON (black) cell.
0, 0, 2, 4, 10, 12, 20, 24, 38, 48, 60, 68, 88, 100, 118, 128, 158, 184, 212, 236, 268, 284, 314, 328, 372, 408, 446, 476, 522, 548, 588, 608, 670, 728, 788, 844, 908, 956, 1018, 1064, 1136, 1192, 1250, 1292, 1366, 1412, 1472, 1504, 1596, 1680, 1766, 1844
Offset: 0
Examples
From _Michael De Vlieger_, Dec 09 2015: (Start)
First 12 rows, replacing "1" with ".", ignoring "0" outside of range of 1's for better visibility of OFF cells, followed by total number of OFF cells per row and running total up to that row:
. = 0 -> 0
. . . = 0 -> 0
. 0 . 0 . = 2 -> 2
. . 0 . 0 . . = 2 -> 4
. 0 0 0 . 0 0 0 . = 6 -> 10
. . . 0 . . . 0 . . . = 2 -> 12
. 0 . 0 0 0 . 0 0 0 . 0 . = 8 -> 20
. . 0 . . 0 . . . 0 . . 0 . . = 4 -> 24
. 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 . = 14 -> 38
. . . 0 0 0 0 0 . . . 0 0 0 0 0 . . . = 10 -> 48
. 0 . 0 . 0 0 0 . 0 . 0 . 0 0 0 . 0 . 0 . = 12 -> 60
. . 0 . 0 . . 0 . . 0 . 0 . . 0 . . 0 . 0 . . = 8 -> 68
. 0 0 0 . 0 0 0 0 0 0 0 . 0 0 0 0 0 0 0 . 0 0 0 . = 20 -> 88
(End)
References
- S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
Links
- Robert Price, Table of n, a(n) for n = 0..999
- Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
- Index entries for sequences related to cellular automata
- Index to Elementary Cellular Automata
Crossrefs
Cf. A071036.
Programs
-
Mathematica
lim = 51; a = {}; Do[AppendTo[a, Take[#, 2 (k - 1) + 1] &@ Take[#[[k]], -(lim + k)]], {k, Length@ #}] &@ CellularAutomaton[150, {{1}, 0}, lim]; Accumulate[Count[#, n_ /; n == 0] & /@ a] (* Michael De Vlieger, Dec 09 2015 *)