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A266793
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Total number of ON (black) cells after n iterations of the "Rule 61" elementary cellular automaton starting with a single ON (black) cell.
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1
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1, 3, 5, 10, 14, 21, 26, 37, 42, 57, 62, 81, 86, 109, 114, 141, 146, 177, 182, 217, 222, 261, 266, 309, 314, 361, 366, 417, 422, 477, 482, 541, 546, 609, 614, 681, 686, 757, 762, 837, 842, 921, 926, 1009, 1014, 1101, 1106, 1197, 1202, 1297, 1302, 1401, 1406
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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 04 2016 and Apr 18 2019: (Start)
a(n) = (1+7*(-1)^n-2*(-3+(-1)^n)*n+2*n^2)/4 for n>3.
a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>8.
G.f.: (1+2*x+x^3+x^4-x^5-x^6+2*x^7-x^8) / ((1-x)^3*(1+x)^2).
(End)
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MATHEMATICA
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rule=61; 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,easy
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AUTHOR
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STATUS
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approved
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