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A136016
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a(n) = 9*n^2-1.
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6
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8, 35, 80, 143, 224, 323, 440, 575, 728, 899, 1088, 1295, 1520, 1763, 2024, 2303, 2600, 2915, 3248, 3599, 3968, 4355, 4760, 5183, 5624, 6083, 6560, 7055, 7568, 8099, 8648, 9215, 9800, 10403, 11024, 11663, 12320, 12995, 13688, 14399, 15128, 15875, 16640
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OFFSET
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1,1
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LINKS
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FORMULA
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G.f.: x*(-8-11*x+x^2) / ( x-1 )^3 . - R. J. Mathar, Jul 01 2011
Sum_{n>=1} 1/a(n) = 1/2 - sqrt(3)*Pi/18.
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/9 - 1/2. (End)
Product_{n>=1} (1 + 1/a(n)) = 2*Pi/(3*sqrt(3)) (A248897).
Product_{n>=1} (1 - 1/a(n)) = sqrt(2/3)*sin(sqrt(2)*Pi/3). (End)
a(n) = a(-n) for all n in Z. Sum_{n in Z} 1/a(n) = -Pi/3^(3/2) = -A073010. - Michael Somos, May 21 2023
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MATHEMATICA
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Table[9n^2 - 1, {n, 1, 100}]
LinearRecurrence[{3, -3, 1}, {8, 35, 80}, 50] (* Harvey P. Dale, Oct 09 2012 *)
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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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