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
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
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 20 2015
STATUS
approved