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 20 2016 and Apr 17 2019: (Start)
a(n) = 11*a(n-1)+9990*a(n-2)-110000*a(n-3)+100000*a(n-4) for n>4.
G.f.: (1-10000*x^2+100000*x^3-100000*x^4) / ((1-x)*(1-10*x)*(1-100*x)*(1+100*x)).
(End)
Conjecture: a(n) = (10*10^n*(10^n + 1)/11 - 1)/9 for odd n; a(n) = (10^n*(10^n + 10)/11 - 1)/9 for even n > 0. - Karl V. Keller, Jr., May 05 2022
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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 17 2016
STATUS
approved