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A008724
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a(n) = floor(n^2/12).
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12
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0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 21, 24, 27, 30, 33, 36, 40, 44, 48, 52, 56, 60, 65, 70, 75, 80, 85, 90, 96, 102, 108, 114, 120, 126, 133, 140, 147, 154, 161, 168, 176, 184, 192, 200, 208, 216, 225, 234, 243, 252, 261, 270, 280, 290, 300, 310, 320, 330, 341, 352
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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COMMENTS
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With a different offset, Molien series for 3-dimensional group [2,n] = *22n.
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n+2} floor(j/6), a(n-2) = (1/2)*floor(n/6)*(2*n - 4 - 6*floor(n/6)). - Mitch Harris, Sep 08 2008
G.f.: x^4/((1-x)^2*(1-x^6)).
Sum_{n>=4} 1/a(n) = Pi^2/18 - Pi/(2*sqrt(3)) + 49/12. - Amiram Eldar, Aug 14 2022
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MAPLE
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floor(n^2/12) ;
end proc:
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MATHEMATICA
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PROG
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(Magma) a008724:=func< n | Floor(n^2/12) >; [ a008724(n): n in [0..70] ];
(Sage) [floor(n^2/12) for n in (0..70)] # G. C. Greubel, Sep 09 2019
(GAP) List([0..70], n-> Int(n^2/12) ); # G. C. Greubel, Sep 09 2019
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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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