login
A266446
Decimal representation of the middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
2
1, 2, 4, 8, 17, 34, 69, 138, 277, 555, 1110, 2220, 4440, 8881, 17762, 35525, 71050, 142101, 284202, 568405, 1136810, 2273621, 4547242, 9094485, 18188970, 36377941, 72755882, 145511765, 291023530, 582047061, 1164094122, 2328188245, 4656376490, 9312752981
OFFSET
0,2
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