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A085001
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a(n) = (3*n+1)*(3*n+4).
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3
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4, 28, 70, 130, 208, 304, 418, 550, 700, 868, 1054, 1258, 1480, 1720, 1978, 2254, 2548, 2860, 3190, 3538, 3904, 4288, 4690, 5110, 5548, 6004, 6478, 6970, 7480, 8008, 8554, 9118, 9700, 10300, 10918, 11554, 12208, 12880, 13570, 14278, 15004
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OFFSET
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0,1
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REFERENCES
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L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 38.
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LINKS
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FORMULA
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Sum_{k=0..n} 3/a(k) = 3*(n+1)/(3n+4). [Corrected by Gary Detlefs, Mar 14 2018]
Sum_{k>=0} 3/a(k) = 1.
Sum_{k>=0} 1/a(k) = 1/3.
Sum_{k=0..n} 1/a(k) = (n+1)/(3n+4) [Jolley]. (End) [Corrected by Gary Detlefs, Mar 14 2018]
Sum_{n>=0} (-1)^n/a(n) = 2*Pi/(9*sqrt(3)) + 2*log(2)/9 - 1/3. - Amiram Eldar, Oct 08 2023
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MATHEMATICA
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CoefficientList[Series[2*(2+8x-x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *)
Table[(3n+1)(3n+4), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {4, 28, 70}, 50] (* Harvey P. Dale, Apr 07 2019 *)
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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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