OFFSET
0,3
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Robert Price, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
FORMULA
Conjectures from Colin Barker, Jan 14 2016: (Start)
a(n) = (2*(-1)^n*n+2*n-9*(-1)^n-1)/2 for n>4.
G.f.: x*(1+2*x+x^4+x^5-2*x^6+x^7) / ((1-x)^2*(1+x)^2).
(End)
MATHEMATICA
rule=111; 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
AUTHOR
Robert Price, Jan 12 2016
STATUS
approved
