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A266072 Number of ON (black) cells in the n-th iteration of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell. 3
1, 1, 1, 5, 1, 9, 1, 13, 1, 17, 1, 21, 1, 25, 1, 29, 1, 33, 1, 37, 1, 41, 1, 45, 1, 49, 1, 53, 1, 57, 1, 61, 1, 65, 1, 69, 1, 73, 1, 77, 1, 81, 1, 85, 1, 89, 1, 93, 1, 97, 1, 101, 1, 105, 1, 109, 1, 113, 1, 117, 1, 121, 1, 125, 1, 129, 1, 133, 1, 137, 1, 141 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

This sequence is A000012 and A016813 interspersed.

Also column 1 of A271343. - Omar E. Pol, Apr 06 2016

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..2000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

FORMULA

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

Conjectures from Colin Barker, Dec 21 2015: (Start)

a(n) = n-(-1)^n*(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 ON cells, followed by the total number of 1's per row:

                      1                        =  1

                    1 . .                      =  1

                  . . . 1 .                    =  1

                1 1 1 1 . . 1                  =  5

              . . . . . . 1 . .                =  1

            1 1 1 1 1 1 1 . . 1 1              =  9

          . . . . . . . . . 1 . . .            =  1

        1 1 1 1 1 1 1 1 1 1 . . 1 1 1          = 13

      . . . . . . . . . . . . 1 . . . .        =  1

    1 1 1 1 1 1 1 1 1 1 1 1 1 . . 1 1 1 1      = 17

  . . . . . . . . . . . . . . . 1 . . . . .    =  1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . 1 1 1 1 1  = 21

(End)

MATHEMATICA

rule = 3; rows = 30; Table[Total[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}]

CROSSREFS

Cf. A000012, A016813, A271343.

Sequence in context: A115521 A140705 A336053 * A147423 A147085 A046580

Adjacent sequences:  A266069 A266070 A266071 * A266073 A266074 A266075

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 20 2015

STATUS

approved

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Last modified August 8 14:36 EDT 2020. Contains 336298 sequences. (Running on oeis4.)