OFFSET
0,4
COMMENTS
Also column 1 of A271343. - Omar E. Pol, Apr 06 2016
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectured g.f.: (1 + x - x^2 + 3*x^3)/(-1 + x^2)^2. - Michael De Vlieger, Dec 21 2015
Conjectures from Colin Barker, Dec 21 2015: (Start)
a(n) = n-(-1)^n*(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 ON cells, followed by the total number of 1's per row:
1 = 1
1 . . = 1
. . . 1 . = 1
1 1 1 1 . . 1 = 5
. . . . . . 1 . . = 1
1 1 1 1 1 1 1 . . 1 1 = 9
. . . . . . . . . 1 . . . = 1
1 1 1 1 1 1 1 1 1 1 . . 1 1 1 = 13
. . . . . . . . . . . . 1 . . . . = 1
1 1 1 1 1 1 1 1 1 1 1 1 1 . . 1 1 1 1 = 17
. . . . . . . . . . . . . . . 1 . . . . . = 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . 1 1 1 1 1 = 21
(End)
MATHEMATICA
rule = 3; 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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 20 2015
STATUS
approved