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 14 2016 and Apr 19 2019: (Start)
a(n) = ((-4)^n+(-1)^n+2^(2*n+1)-1)/2 for n>1.
a(n) = 17*a(n-2)-16*a(n-4) for n>5.
G.f.: (1+3*x+7*x^2-20*x^3-8*x^4+32*x^5) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
MATHEMATICA
rule=117; 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[FromDigits[catri[[k]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Price, Jan 12 2016
EXTENSIONS
Removed an unjustified claim that Colin Barker's conjectures are correct. Removed a program based on a conjecture. - Michael De Vlieger, Jun 13 2022
STATUS
approved