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A267255
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Decimal representation of the n-th iteration of the "Rule 111" elementary cellular automaton starting with a single ON (black) cell.
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3
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1, 6, 7, 122, 31, 2018, 95, 32738, 95, 524258, 95, 8388578, 95, 134217698, 95, 2147483618, 95, 34359738338, 95, 549755813858, 95, 8796093022178, 95, 140737488355298, 95, 2251799813685218, 95, 36028797018963938, 95, 576460752303423458, 95, 9223372036854775778
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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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a(n) = 17*a(n-2)-16*a(n-4) for n>8.
G.f.: (1+6*x-10*x^2+20*x^3-72*x^4+40*x^5-320*x^6+384*x^7-1024*x^8) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)).
(End)
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MATHEMATICA
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rule=111; 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]], 2], {k, 1, rows}] (* Decimal Representation of Rows *)
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PROG
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(Python) print([1, 6, 7, 122, 31] + [2*4**n - 30 if n%2 else 95 for n in range(5, 50)]) # Karl V. Keller, Jr., Sep 12 2021
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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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STATUS
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approved
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