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A266074
Total number of OFF (white) cells after n iterations of the "Rule 3" elementary cellular automaton starting with a single ON (black) cell.
2
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.
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
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 20 2015
STATUS
approved