A266074 Total number of OFF (white) cells after n iterations of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.

0, 2, 6, 8, 16, 18, 30, 32, 48, 50, 70, 72, 96, 98, 126, 128, 160, 162, 198, 200, 240, 242, 286, 288, 336, 338, 390, 392, 448, 450, 510, 512, 576, 578, 646, 648, 720, 722, 798, 800, 880, 882, 966, 968, 1056, 1058, 1150, 1152, 1248, 1250, 1350, 1352, 1456

Offset: 0

Author

Robert Price, Dec 20 2015

Keywords

• nonn
• easy

Examples

			From _Michael De Vlieger_, Dec 21 2015: (Start)
First 12 rows, replacing "1" with "." for better visibility of OFF cells, followed by the total number of 0's per row, then the running total up to and including that row:
                      .                        =  0  ->  0
                    . 0 0                      =  2  ->  2
                  0 0 0 . 0                    =  4  ->  6
                . . . . 0 0 .                  =  2  ->  8
              0 0 0 0 0 0 . 0 0                =  8  -> 16
            . . . . . . . 0 0 . .              =  2  -> 18
          0 0 0 0 0 0 0 0 0 . 0 0 0            = 12  -> 30
        . . . . . . . . . . 0 0 . . .          =  2  -> 32
      0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0        = 16  -> 48
    . . . . . . . . . . . . . 0 0 . . . .      =  2  -> 50
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 . 0 0 0 0 0    = 20  -> 70
. . . . . . . . . . . . . . . . 0 0 . . . . .  =  2  -> 72
(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. A135276.

Formula

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

Empirical a(n) = 1/4*(2*n^2 + 2*(-1)^n*n + 6*n - (-1)^n + 1). - Colin Barker, Dec 21 2015

a(n) = 2*A135276(n). - Alois P. Heinz, Dec 21 2015