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A004538
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a(n) = 3*n^2 + 3*n - 1.
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3
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-1, 5, 17, 35, 59, 89, 125, 167, 215, 269, 329, 395, 467, 545, 629, 719, 815, 917, 1025, 1139, 1259, 1385, 1517, 1655, 1799, 1949, 2105, 2267, 2435, 2609, 2789, 2975, 3167, 3365, 3569, 3779, 3995, 4217, 4445
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OFFSET
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0,2
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COMMENTS
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Numbers k such that (4*k + 7)/3 is a square. - Bruno Berselli, Sep 11 2018
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LINKS
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FORMULA
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a(n) = 5 * Sum_{k=1..n} k^4 / Sum_{k=1..n} k^2, n > 0.
G.f.: (-1 + 8*x - x^2)/(1 - x)^3.
E.g.f.: (-1 + 6*x + 3*x^2)*exp(x). (End)
Sum_{n>=0} 1/a(n) = ( psi(1/2+sqrt(21)/6) - psi(1/2-sqrt(21)/6)) /sqrt(21) = -0.6286929... R. J. Mathar, Apr 24 2024
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MATHEMATICA
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Table[5*Sum[k^4, {k, 1, n}]/Sum[k^2, {k, 1, n}], {n, 1, 20}] (* Alexander Adamchuk, Apr 12 2006 *)
Table[3n^2+3n-1, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {-1, 5, 17}, 40] (* Harvey P. Dale, Jan 18 2019 *)
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PROG
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(Magma) [3*n^2 + 3*n -1: n in [0..50]]; // G. C. Greubel, Sep 10 2018
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CROSSREFS
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KEYWORD
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sign,easy,changed
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AUTHOR
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STATUS
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approved
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