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A046162
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Reduced numerators of (n-1)^2/(n^2 + n + 1).
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3
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0, 1, 4, 3, 16, 25, 12, 49, 64, 27, 100, 121, 48, 169, 196, 75, 256, 289, 108, 361, 400, 147, 484, 529, 192, 625, 676, 243, 784, 841, 300, 961, 1024, 363, 1156, 1225, 432, 1369, 1444, 507, 1600, 1681, 588, 1849, 1936, 675, 2116, 2209, 768, 2401, 2500
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OFFSET
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1,3
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COMMENTS
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Arises in Routh's theorem.
With offset 0, multiplicative with a(3^e) = 3^(2e-1), a(p^e) = p^(2e) otherwise. - David W. Wilson, Jun 12 2005, corrected by Robert Israel, Apr 28 2017
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LINKS
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FORMULA
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G.f.: x^2*(1 + 4*x + 3*x^2 + 13*x^3 + 13*x^4 + 3*x^5 + 4*x^6 + x^7)/(1 - x^3)^3.
a(n) = numerator((n-1)^2/3).
Sum_{n>=2} 1/a(n) = 11*Pi^2/54. (End)
With offset 0, Dirichlet g.f.: zeta(s-2)*(1-6/3^s).
Sum_{k=1..n} a(k) ~ 7*n^3/27. (End)
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MAPLE
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MATHEMATICA
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a[n_] := Numerator[(n - 1)^2/(n^2 + n + 1)]; Array[a, 50] (* Amiram Eldar, Aug 11 2022 *)
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PROG
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(Magma) [Numerator((n-1)^2/3): n in [1..70]]; // G. C. Greubel, Oct 27 2022
(SageMath) [numerator((n-1)^2/3) for n in range(1, 71)] # G. C. Greubel, Oct 27 2022
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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