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1, 6, 24, 96, 372, 1416, 5340, 20040, 75012, 280392, 1047324, 3910440, 14597508, 54485736, 203357724, 758969736, 2832570372, 10571410056, 39453266460, 147242049000, 549515715972, 2050822387752, 7653776980764, 28564291826760, 106603402909188, 397849344975816, 1484794027325724, 5541326864990376
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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N. J. A. Sloane, On the No. of ON Cells in Cellular Automata, Video of talk in Doron Zeilberger's Experimental Math Seminar at Rutgers University, Feb. 05 2015: Part 1, Part 2
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FORMULA
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G.f.: (1-3*x^2+4*x^3) / ((1-2*x)*(1-4*x+x^2)).
a(n) = -2^n + 2*(2-sqrt(3))^n + 2*(2+sqrt(3))^n for n>0.
a(n) = 6*a(n-1) - 9*a(n-2) + 2*a(n-3) for n>3.
(End)
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MATHEMATICA
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PROG
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(PARI) Vec((1-3*x^2+4*x^3) / ((1-2*x)*(1-4*x+x^2)) + O(x^30)) \\ Colin Barker, Feb 04 2017
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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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