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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 12 19:33 EST 2019. Contains 329078 sequences. (Running on oeis4.)