A266073 Number of OFF (white) cells in the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 4, 2, 8, 2, 12, 2, 16, 2, 20, 2, 24, 2, 28, 2, 32, 2, 36, 2, 40, 2, 44, 2, 48, 2, 52, 2, 56, 2, 60, 2, 64, 2, 68, 2, 72, 2, 76, 2, 80, 2, 84, 2, 88, 2, 92, 2, 96, 2, 100, 2, 104, 2, 108, 2, 112, 2, 116, 2, 120, 2, 124, 2, 128, 2, 132, 2, 136, 2, 140, 2

Offset: 0

Author

Robert Price, Dec 20 2015

Keywords

• nonn
• easy

Examples

			From _Michael De Vlieger_, Dec 21 2015: (Start)
First 12 rows, replacing "0" with "." for better visibility of OFF cells, followed by the total number of 0's per row:
                      .                        =  0
                    . 0 0                      =  2
                  0 0 0 . 0                    =  4
                . . . . 0 0 .                  =  2
              0 0 0 0 0 0 . 0 0                =  8
            . . . . . . . 0 0 . .              =  2
          0 0 0 0 0 0 0 0 0 . 0 0 0            = 12
        . . . . . . . . . . 0 0 . . .          =  2
      0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0        = 16
    . . . . . . . . . . . . . 0 0 . . . .      =  2
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0    = 20
. . . . . . . . . . . . . . . . 0 0 . . . . .  =  2
(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

Formula

Empirical g.f.: (-2*(-x - 2*x^2 + x^3))/(-1 + x^2)^2. - Michael De Vlieger, Dec 21 2015

Conjectures from Colin Barker, Dec 21 2015 and Apr 17 2019: (Start)

a(n) = (-1)^n*n+n-(-1)^n+1.

a(n) = 2*a(n-2) - a(n-4) for n>3.

(End)