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

0,2

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)

Example

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)

Crossrefs

Sequence in context: A209675 A307669 A171977 * A059866 A278262 A093895

Adjacent sequences: A266070 A266071 A266072 * A266074 A266075 A266076

Keyword

nonn,easy

Author

Robert Price, Dec 20 2015

Status

approved