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A267154
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Decimal representation of the n-th iteration of the "Rule 107" elementary cellular automaton starting with a single ON (black) cell.
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2
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1, 4, 11, 110, 119, 1978, 475, 32510, 1799, 523002, 6939, 8388350, 1799, 134216442, 6939, 2147483390, 1799, 34359737082, 6939, 549755813630, 1799, 8796093020922, 6939, 140737488355070, 1799, 2251799813683962, 6939, 36028797018963710, 1799, 576460752303422202
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OFFSET
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0,2
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REFERENCES
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S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
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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) = 16*a(n-2)+a(n-4)-16*a(n-6) for n>12.
G.f.: (1+4*x-5*x^2+46*x^3-58*x^4+214*x^5-1424*x^6+816*x^7-5744*x^8 +2624*x^9 -20416*x^10 +19456*x^11 -103424*x^12) / ((1-x)*(1+x)*(1-4*x)*(1+4*x)*(1+x^2)).
(End)
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MATHEMATICA
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rule=107; 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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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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