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, Dec 30 2015 and Apr 16 2019: (Start)
a(n) = (-(-1)^n+6661*2^(n-10)-3)/6 for n>10.
G.f.: (1-x^2+x^4+x^9-x^10-x^11+x^13) / ((1-x)*(1+x)*(1-2*x)).
(End)
Conjecture: a(n) = floor(6661*2^n/6144). - Karl V. Keller, Jr., Dec 26 2021
MATHEMATICA
rule=25; 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, Dec 29 2015
STATUS
approved