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 17 2016 and Apr 20 2019: (Start)
a(n) = 3*a(n-1)-2*a(n-2) for n > 4. [n range correction by Karl V. Keller, Jr., Apr 14 2022]
G.f.: (1-x^2+x^4) / ((1-x)*(1-2*x)).
(End)
{1,3,6} followed by A198274 (conjectured). - Robert Price, Jan 17 2016
MATHEMATICA
rule=143; 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 *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* keep only middle cell from each row *) Table[FromDigits[Take[mc, k], 2], {k, 1, rows}] (* binary representation of middle column *)
PROG
(PARI) a(n) = bitneg(3<<(n-3), n+1); \\ Kevin Ryde, Apr 15 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 16 2016
STATUS
approved