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

0,2

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)^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

Example

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)

Crossrefs

Cf. A135276.

Sequence in context: A306906 A174658 A326300 * A191822 A238549 A237502

Adjacent sequences: A266071 A266072 A266073 * A266075 A266076 A266077

Keyword

nonn,easy

Author

Robert Price, Dec 20 2015

Status

approved