OFFSET
0,4
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Dec 14 2015 and Apr 16 2019: (Start)
a(n) = 1/2*(-2*(-1)^n*n+2*n+3*(-1)^n-1).
a(n) = 2*a(n-2) - a(n-4) for n>3.
G.f.: (1-x^2+4*x^3) / ((1-x)^2*(1+x)^2).
(End)
a(n) = A019425(n), n>1. - R. J. Mathar, Jan 10 2016
EXAMPLE
From Michael De Vlieger, Dec 14 2015: (Start)
First 12 rows, replacing zeros with "." for better visibility of ON cells, followed by the total number of 1's per row at right:
1 = 1
. . . = 0
. . 1 . . = 1
1 1 . . . 1 1 = 4
. . . . 1 . . . . = 1
1 1 1 1 . . . 1 1 1 1 = 8
. . . . . . 1 . . . . . . = 1
1 1 1 1 1 1 . . . 1 1 1 1 1 1 = 12
. . . . . . . . 1 . . . . . . . . = 1
1 1 1 1 1 1 1 1 . . . 1 1 1 1 1 1 1 1 = 16
. . . . . . . . . . 1 . . . . . . . . . . = 1
1 1 1 1 1 1 1 1 1 1 . . . 1 1 1 1 1 1 1 1 1 1 = 20
(End)
MATHEMATICA
rule = 1; 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 14 2015
STATUS
approved