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A267452
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Total number of ON (black) cells after n iterations of the "Rule 131" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 2, 4, 6, 10, 13, 19, 24, 30, 37, 46, 53, 63, 73, 84, 95, 108, 120, 135, 149, 164, 180, 198, 214, 233, 252, 272, 292, 314, 335, 359, 382, 406, 431, 458, 483, 511, 539, 568, 597, 628, 658, 691, 723, 756, 790, 826, 860, 897, 934, 972, 1010, 1050, 1089, 1131
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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 15 2016 and Apr 19 2019: (Start)
a(n) = a(n-1)+a(n-3)-a(n-5)-a(n-7)+a(n-8) for n>7.
G.f.: (1+x+2*x^2+x^3+2*x^4+2*x^6) / ((1-x)^3*(1+x)*(1+x^2)*(1+x+x^2)).
(End)
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MATHEMATICA
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rule=131; 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 *) nbc=Table[Total[catri[[k]]], {k, 1, rows}]; (* Number of Black cells in stage n *) Table[Total[Take[nbc, k]], {k, 1, rows}] (* Number of Black cells through stage n *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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