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A126264
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a(n) = 5*n^2 + 3*n.
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3
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8, 26, 54, 92, 140, 198, 266, 344, 432, 530, 638, 756, 884, 1022, 1170, 1328, 1496, 1674, 1862, 2060, 2268, 2486, 2714, 2952, 3200, 3458, 3726, 4004, 4292, 4590, 4898, 5216, 5544, 5882, 6230, 6588, 6956, 7334, 7722, 8120, 8528, 8946, 9374, 9812, 10260
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OFFSET
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1,1
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REFERENCES
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L. B. W. Jolley, Summation of Series, Dover Publications, 1961, p. 12
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LINKS
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FORMULA
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Sum_{i=1..n} a(i) = n*(n+1)*(5n+7)/3 = 2*A162148(n).
G.f.: 2*x*(x + 4)/(1 - x)^3.
E.g.f.: x*(5*x + 8)*exp(x). (End)
Sum_{n>=1} 1/a(n) = 5/9 + sqrt(1-2/sqrt(5))*Pi/6 + log(phi)*sqrt(5)/6 - 5*log(5)/12, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 21 2022
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EXAMPLE
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a(24) = 5*24^2 + 3*24 = 2880 + 72 = 2952.
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MAPLE
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MATHEMATICA
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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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