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A179741
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a(n) = (2*n+1)*(6*n-1).
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2
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-1, 15, 55, 119, 207, 319, 455, 615, 799, 1007, 1239, 1495, 1775, 2079, 2407, 2759, 3135, 3535, 3959, 4407, 4879, 5375, 5895, 6439, 7007, 7599, 8215, 8855, 9519, 10207, 10919, 11655, 12415, 13199, 14007, 14839, 15695, 16575, 17479, 18407
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = a(n-1) + 24*n + 16.
a(n) = 2*a(n-1) - a(n-2) + 16.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (-1 +18*x +7*x^2)/(1-x)^3.
E.g.f.: (-1 + 16*x + 12*x^2)*exp(x). - G. C. Greubel, Jul 22 2017
Sum_{n>=1} 1/a(n) = (3*log(3) - Pi*sqrt(3) + 4)/16.
Sum_{n>=1} (-1)^(n+1)/a(n) = (3*Pi - 2*sqrt(3)*log(sqrt(3)+2) - 4)/16. (End)
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MATHEMATICA
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Table[12n^2+4n-1, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {-1, 15, 55}, 40] (* Harvey P. Dale, Dec 17 2013 *)
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PROG
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CROSSREFS
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KEYWORD
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sign,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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