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A267138
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Binary representation of the n-th iteration of the "Rule 103" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 110, 110, 1110101, 111100, 11110001011, 101111000, 111111100010111, 1011110000, 1111111111000101111, 10111100000, 11111111111110001011111, 101111000000, 111111111111111100010111111, 1011110000000, 1111111111111111111000101111111, 10111100000000
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OFFSET
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0,2
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LINKS
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FORMULA
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Conjectures from Colin Barker, Jan 11 2016 and Apr 19 2019: (Start)
a(n) = 10011*a(n-2) - 110010*a(n-4) + 100000*a(n-6) for n > 10.
G.f.: (1 + 110*x - 9901*x^2 + 8891*x^3 - 880100*x^4 + 8881000*x^5 - 999110000*x^6 + 10991100000*x^7 - 999000000000*x^8 - 11000000000*x^9 + 1000000000000*x^10) / ((1-x)*(1+x)*(1-100*x)*(1+100*x)*(1-10*x^2)). (End)
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MATHEMATICA
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rule=103; 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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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