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 19 2016: (Start)
a(n) = 6*a(n-1)-7*a(n-2)-6*a(n-3)+8*a(n-4) for n>5.
G.f.: (1-4*x+15*x^2+4*x^3-12*x^4-16*x^5) / ((1-x)*(1+x)*(1-2*x)*(1-4*x)).
(End)
Conjecture: a(n) = 2*(-3 + (-1)^n - 2^(2+n) + 3*4^n)/3 for n>1. - Colin Barker, Feb 14 2017
Conjecture: a(n) = floor((6*4^n - 8*2^n)/3) - 2^(n mod 2) for n > 1. - Karl V. Keller, Jr., Jun 01 2022
MATHEMATICA
rule=197; 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 19 2016
STATUS
approved