OFFSET
0,2
LINKS
Robert Price, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Jan 05 2016 and Apr 18 2019: (Start)
a(n) = 11001*a(n-2) - 10011000*a(n-4) + 10000000*a(n-6) for n > 9.
G.f.: (1 + 100*x - 9991*x^2 - 99*x^3 - 88910*x^4 - 9990*x^5 - 10901100*x^6 - 99900*x^7 + 11000000*x^8 - 1000000*x^9) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-1000*x^2)).
(End)
Conjecture: a(n) = (10*100^n - 999909*1000^floor(n/2)/10000 - 1)/9 for odd n > 3; a(n) = 10111*1000^(n/2)/10000 for even n > 3. - Karl V. Keller, Jr., Dec 16 2021
MATHEMATICA
rule=67; 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]]], {k, 1, rows}] (* Binary Representation of Rows *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 04 2016
STATUS
approved