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
Conjectures from Colin Barker, Dec 09 2015 and Apr 16 2019: (Start)
a(n) = (1/8)*(6*n-3*(-1)^n+(1-i)*(-i)^n+(1+i)*i^n+9) where i = sqrt(-1).
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 4.
G.f.: (1+x+2*x^3-x^4) / ((1-x)^2*(1+x)*(1+x^2)). (End)
a(n) = (6*n+9+2*cos(n*Pi/2)-3*cos(n*Pi)-2*sin(n*Pi/2))/8. - Wesley Ivan Hurt, Oct 02 2017
EXAMPLE
From Michael De Vlieger, Dec 09 2015: (Start)
First 12 rows, replacing "0" with ".", ignoring "0" outside of range of 1's for better visibility of ON cells, with total number of 1's in the row to the left of the chart:
1 = 1
2 = 1 1
2 = 1 . 1
4 = 1 1 1 1
4 = 1 1 1 . 1
5 = 1 1 . 1 1 1
5 = 1 . 1 1 1 . 1
7 = 1 1 1 1 . 1 1 1
7 = 1 1 1 . 1 1 1 . 1
8 = 1 1 . 1 1 1 . 1 1 1
8 = 1 . 1 1 1 . 1 1 1 . 1
10 = 1 1 1 1 . 1 1 1 . 1 1 1
10 = 1 1 1 . 1 1 1 . 1 1 1 . 1
(End)
MATHEMATICA
rule = 188; 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}]
Count[#, n_ /; n == 1] & /@ CellularAutomaton[188, {{1}, 0}, 66] (* Michael De Vlieger, Dec 09 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 08 2015
STATUS
approved