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A266445
Binary representation of the middle column of the "Rule 25" elementary cellular automaton starting with a single ON (black) cell.
2
1, 10, 100, 1000, 10001, 100010, 1000101, 10001010, 100010101, 1000101011, 10001010110, 100010101100, 1000101011000, 10001010110001, 100010101100010, 1000101011000101, 10001010110001010, 100010101100010101, 1000101011000101010, 10001010110001010101
OFFSET
0,2
REFERENCES
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
FORMULA
Conjectures from Colin Barker, Dec 31 2015 and Apr 16 2019: (Start)
a(n) = (-9*(-1)^n+9901000008901*2^(n-10)*5^(n-11)-11)/198 for n>10.
G.f.: (1-x^2+x^4+x^9-x^10-x^11+x^13) / ((1-x)*(1+x)*(1-10*x)).
(End)
Conjecture: a(n) = floor(9901000008901*10^n/9900000000000). - Karl V. Keller, Jr., Jan 30 2022
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]], {k, 1, rows}] (* Binary Representation of Middle Column *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 29 2015
STATUS
approved