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 13 2016 and Apr 17 2019: (Start)
a(n) = (383*2^n-32*((-1)^n+3))/192 for n>5.
G.f.: (1+x-x^8) / ((1-x)*(1+x)*(1-2*x)).
(End)
MATHEMATICA
rule=111; 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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 12 2016
STATUS
approved