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 27 2015 and Apr 14 2019: (Start)
a(n) = (2*(-1)^n*n+2*n-3*(-1)^n+1)/2 for n>0
a(n) = 2*a(n-2)-a(n-4) for n>4.
G.f.: x*(2+3*x-2*x^2+x^3) / ((1-x)^2*(1+x)^2).
(End)
MATHEMATICA
rule=11; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}] (* Number of White cells in stage n *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 25 2015
EXTENSIONS
Conjectures from Colin Barker, Apr 14 2019
STATUS
approved