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A144449
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a(n) = 4*(4 + 9*n^2 + 15*n).
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2
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16, 112, 280, 520, 832, 1216, 1672, 2200, 2800, 3472, 4216, 5032, 5920, 6880, 7912, 9016, 10192, 11440, 12760, 14152, 15616, 17152, 18760, 20440, 22192, 24016, 25912, 27880, 29920, 32032, 34216, 36472, 38800, 41200, 43672, 46216, 48832, 51520, 54280, 57112
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OFFSET
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0,1
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COMMENTS
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a(n) mod 9 = period 3: repeat 7,4,1 = A070403(n+1).
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LINKS
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FORMULA
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a(n) = a(n-1) + 24*(3*n+1) = a(n-1) + 72*n + 24, a(0)=16.
A061039(6n+2) = A061039(6n-4) + 24*(3n+1) = a(6n-4) + 72*n + 24, a(2)=16.
G.f.: 8*(2 + 8*x - x^2)/(1-x)^3.
E.g.f.: 4*(4 + 24*x + 9*x^2)*exp(x). (End)
Sum_{n>=0} 1/a(n) = 1/12.
Sum_{n>=0} (-1)^n/a(n) = Pi/(18*sqrt(3)) + log(2)/18 - 1/12. (End)
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MATHEMATICA
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Table[36n^2+60n+16, {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {16, 112, 280}, 40] (* Harvey P. Dale, Apr 04 2020 *)
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PROG
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(Sage) [(6*n+5)^2 - 9 for n in (0..40)] # G. C. Greubel, Mar 06 2022
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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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