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) = (1/16)*(6*n^2 + 24*n - 3*(-1)^n + 2*(-i)^n + 2*i^n + 15) where i = sqrt(-1).
G.f.: (1 + x + 2*x^3 - x^4) / ((1-x)^3*(1+x)*(1+x^2)).
(End)
Conjecture: the sequence consists of all numbers k > 0 such that floor(sqrt(8*(k+1)/3)) != floor(sqrt(8*k/3)). - Gevorg Hmayakyan, Sep 01 2019
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, followed by total number of ON cells per row, and running total up to that row:
1 = 1 -> 1
1 1 = 2 -> 3
1 . 1 = 2 -> 5
1 1 1 1 = 4 -> 9
1 1 1 . 1 = 4 -> 13
1 1 . 1 1 1 = 5 -> 18
1 . 1 1 1 . 1 = 5 -> 23
1 1 1 1 . 1 1 1 = 7 -> 30
1 1 1 . 1 1 1 . 1 = 7 -> 37
1 1 . 1 1 1 . 1 1 1 = 8 -> 45
1 . 1 1 1 . 1 1 1 . 1 = 8 -> 53
1 1 1 1 . 1 1 1 . 1 1 1 = 10 -> 63
1 1 1 . 1 1 1 . 1 1 1 . 1 = 10 -> 72
(End)
MATHEMATICA
rule = 188; rows = 30; Table[Total[Take[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}], k]], {k, 1, rows}]
Accumulate[Count[#, n_ /; n == 1] & /@ CellularAutomaton[188, {{1}, 0}, 53]] (* Michael De Vlieger, Dec 09 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 08 2015
STATUS
approved