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A189834
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a(n) = n^2 + 9.
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9
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9, 10, 13, 18, 25, 34, 45, 58, 73, 90, 109, 130, 153, 178, 205, 234, 265, 298, 333, 370, 409, 450, 493, 538, 585, 634, 685, 738, 793, 850, 909, 970, 1033, 1098, 1165, 1234, 1305, 1378, 1453, 1530, 1609, 1690, 1773, 1858, 1945
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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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G.f.: ( -9+17*x-10*x^2 ) / (x-1)^3 . - R. J. Mathar, Aug 31 2011
Sum_{n>=0} 1/a(n) = (1 + 3*Pi*coth(3*Pi))/18.
Sum_{n>=0} (-1)^n/a(n) = (1 + 3*Pi*cosech(3*Pi))/18. (End)
Product_{n>=0} (1 - 1/a(n)) = (2/3)*sqrt(2)*sinh(2*sqrt(2)*Pi)/sinh(3*Pi).
Product_{n>=0} (1 + 1/a(n)) = (sqrt(10)/3)*sinh(sqrt(10)*Pi)/sinh(3*Pi). (End)
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MATHEMATICA
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Table[n^2+9, {n, 0, 100}]
LinearRecurrence[{3, -3, 1}, {9, 10, 13}, 50] (* Harvey P. Dale, Aug 21 2020 *)
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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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