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 16 2016 and Apr 17 2019: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 4.
G.f.: (1 + x^3 + x^4)/((1 - x)^2*(1 + x)). (End)
Conjectured e.g.f.: 2 + x + (3*x/2 - 1)*cosh(x) + 3*(x - 1)*sinh(x)/2. - Stefano Spezia, Feb 20 2023
MATHEMATICA
rule=141; 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, Jan 16 2016
STATUS
approved