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A024202
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a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.
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1
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1, 11, 38, 96, 205, 385, 662, 1068, 1635, 2401, 3410, 4706, 6339, 8365, 10840, 13826, 17391, 21603, 26536, 32270, 38885, 46467, 55108, 64900, 75941, 88335, 102186, 117604, 134705, 153605, 174426, 197296, 222343, 249701, 279510, 311910, 347047, 385073
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OFFSET
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1,2
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LINKS
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FORMULA
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Empirical g.f.: x*(x^4-5*x^3-7*x-1) / ((x-1)^5*(x^2+x+1)). - Colin Barker, Aug 15 2014
a(n) = floor(A024197(n)/(n+2)^2) = floor(n*(n+1)*(n^2+3*n+1)/6).
a(n) = (n^4+4*n^3+4*n^2+n-4)/6 if n == 1 (mod 3).
Otherwise a(n) = n*(n+1)*(n^2+3*n+1)/6.
The empirical g.f. can be obtained from this. (End)
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MAPLE
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f:= proc(n)
if n mod 3 = 1 then (n^4+4*n^3+4*n^2+n-4)/6
else n*(n+1)*(n^2+3*n+1)/6
fi
end proc:
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MATHEMATICA
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Table[Floor[n*(n + 1)*(n^2 + 3*n + 1)/6], {n, 1, 50}] (* G. C. Greubel, Dec 30 2016 *)
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PROG
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(PARI) for(n=1, 25, print1(floor(n*(n+1)*(n^2+3*n+1)/6), ", ")) \\ G. C. Greubel, Dec 30 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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