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A266589
Binary representation of the n-th iteration of the "Rule 37" elementary cellular automaton starting with a single ON (black) cell.
2
1, 10, 1110, 1000001, 111000, 11100000111, 11100000, 111110000011111, 1110000000, 1111111000001111111, 111000000000, 11111111100000111111111, 11100000000000, 111111111110000011111111111, 1110000000000000, 1111111111111000001111111111111, 111000000000000000
OFFSET
0,2
FORMULA
Conjectures from Colin Barker, Jan 01 2016 and Apr 18 2019: (Start)
a(n) = 10101*a(n-2)-1010100*a(n-4)+1000000*a(n-6) for n>7.
G.f.: (1 +10*x -8991*x^2 +898991*x^3 -10091010*x^4 +1009091010*x^5 +10100000*x^6 -1010100000*x^7) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -100*x)*(1 +100*x)).
(End)
Conjecture: a(n) = (10*100^n - 99999*10^(n-2) - 1)/9 for odd n > 1; a(n) = 111*10^(n-1) for even n > 1. - Karl V. Keller, Jr., Oct 06 2021
MATHEMATICA
rule=37; 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 *) Table[FromDigits[catri[[k]]], {k, 1, rows}] (* Binary Representation of Rows *)
CROSSREFS
Sequence in context: A049064 A267246 A355316 * A015026 A130598 A267595
KEYWORD
nonn,easy
AUTHOR
Robert Price, Jan 01 2016
STATUS
approved