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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
OFFSET
0,2
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 20 2015
STATUS
approved