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A267454
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Total number of OFF (white) 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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0, 2, 5, 10, 15, 23, 30, 40, 51, 63, 75, 91, 106, 123, 141, 161, 181, 204, 226, 251, 277, 304, 331, 362, 392, 424, 457, 492, 527, 565, 602, 642, 683, 725, 767, 813, 858, 905, 953, 1003, 1053, 1106, 1158, 1213, 1269, 1326, 1383, 1444, 1504, 1566, 1629, 1694
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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.: x*(2+3*x+5*x^2+3*x^3+3*x^4-x^5) / ((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 *) nwc=Table[Length[catri[[k]]]-nbc[[k]], {k, 1, rows}]; (* Number of White cells in stage n *) Table[Total[Take[nwc, k]], {k, 1, rows}] (* Number of White cells through stage n *)
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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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