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A100705
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a(n) = n^3 + (n+1)^2.
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9
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1, 5, 17, 43, 89, 161, 265, 407, 593, 829, 1121, 1475, 1897, 2393, 2969, 3631, 4385, 5237, 6193, 7259, 8441, 9745, 11177, 12743, 14449, 16301, 18305, 20467, 22793, 25289, 27961, 30815, 33857, 37093, 40529, 44171, 48025, 52097, 56393, 60919, 65681, 70685, 75937
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OFFSET
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0,2
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COMMENTS
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The finite simple continued fraction [1;n-1,n,n+1] has a numerator in the resulting rational number (n^3+2*n+n^2+1)/(n*(n^2+1)) that is the same as a(n). - J. M. Bergot, Sep 29 2011
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LINKS
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FORMULA
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G.f.: ( 1+x+3*x^2+x^3 ) / (x-1)^4 . - R. J. Mathar, Sep 29 2011
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MATHEMATICA
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Table[n^3 + (n + 1)^2, {n, 0, 45}]
LinearRecurrence[{4, -6, 4, -1}, {1, 5, 17, 43}, 50] (* Harvey P. Dale, Dec 03 2014 *)
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PROG
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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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