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..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Dec 28 2015 and Apr 14 2019: (Start)
a(n) = ((-1)^n*(3-2*n)+4*n+1)/4.
a(n) = 2*a(n-2)-a(n-4) for n>3.
G.f.: (1+x+2*x^3) / ((1-x)^2*(1+x)^2).
(End)
MATHEMATICA
rule=13; 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 *) Table[Total[catri[[k]]], {k, 1, rows}] (* Number of Black cells in stage n *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 26 2015
EXTENSIONS
Conjectures from Colin Barker, Apr 14 2019
STATUS
approved