A265223 - OEIS

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

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

OFFSET

0,3

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

EXAMPLE

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)

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 *)

CROSSREFS

Cf. A071036.

Sequence in context: A071642 A226827 A266538 * A034166 A301338 A364667

Adjacent sequences: A265220 A265221 A265222 * A265224 A265225 A265226

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 07 2015

STATUS

approved