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1, 5, 25, 101, 361, 1205, 3865, 12101, 37321, 114005, 346105, 1046501, 3155881, 9500405, 28566745, 85831301, 257756041, 773792405, 2322425785, 6969374501, 20912317801, 62745342005, 188252803225, 564791964101, 1694443001161, 5083463221205, 15250658099065
(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-x+6*x^2) / ((1-x)*(1-2*x)*(1-3*x)).
a(n) = (3 - 2^(3+n) + 2*3^(1+n)).
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>2.
(End)
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MATHEMATICA
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PROG
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(PARI) Vec((1-x+6*x^2) / ((1-x)*(1-2*x)*(1-3*x)) + O(x^30)) \\ Colin Barker, Feb 03 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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STATUS
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approved
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