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A152161
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a(n) = 100*n^2 + 100*n + 21.
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2
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21, 221, 621, 1221, 2021, 3021, 4221, 5621, 7221, 9021, 11021, 13221, 15621, 18221, 21021, 24021, 27221, 30621, 34221, 38021, 42021, 46221, 50621, 55221, 60021, 65021, 70221, 75621, 81221, 87021, 93021, 99221, 105621, 112221, 119021, 126021, 133221, 140621, 148221
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OFFSET
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0,1
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = sqrt(5-2*sqrt(5))*Pi/40.
Sum_{n>=0} (-1)^n/a(n) = (sqrt(10-2*sqrt(5))*log(cot(Pi/20)) + sqrt(10+2*sqrt(5))*log(tan(3*Pi/20)))/40.
Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/10)/phi, where phi is the golden ratio (A001622).
Product_{n>=0} (1 + 1/a(n)) = 2*cos(sqrt(3)*Pi/10)/phi. (End)
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MATHEMATICA
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Table[100*n^2 + 100*n + 21, {n, 0, 50}] (* G. C. Greubel, Sep 20 2018 *)
LinearRecurrence[{3, -3, 1}, {21, 221, 621}, 40] (* Harvey P. Dale, Dec 06 2018 *)
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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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STATUS
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approved
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