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..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
FORMULA
Conjectures from Colin Barker, Jan 20 2016 and Apr 16 2019: (Start)
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>3.
G.f.: (1+x+x^3) / ((1-x)^3*(1+x)).
(End)
MATHEMATICA
rule=157; 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[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 17 2016
STATUS
approved