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A168277
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a(n) = 2*n - (-1)^n - 2.
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7
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1, 1, 5, 5, 9, 9, 13, 13, 17, 17, 21, 21, 25, 25, 29, 29, 33, 33, 37, 37, 41, 41, 45, 45, 49, 49, 53, 53, 57, 57, 61, 61, 65, 65, 69, 69, 73, 73, 77, 77, 81, 81, 85, 85, 89, 89, 93, 93, 97, 97, 101, 101, 105, 105, 109, 109, 113, 113, 117, 117, 121, 121, 125, 125, 129, 129
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = 4*n - a(n-1) - 6, with n>1, a(1)=1.
G.f.: x*(1 + 3*x^2)/( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 15 2013
E.g.f.: (-1 + 3*exp(x) + 2*(x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016
Sum_{n>=1} 1/a(n)^2 = Pi^2/8 + G, where G is Catalan's constant (A006752). - Amiram Eldar, Aug 21 2022
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MATHEMATICA
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CoefficientList[Series[(1 + 3 x^2) / ((1 + x) (x - 1)^2), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 16 2013 *)
LinearRecurrence[{1, 1, -1}, {1, 1, 5}, 70] (* Harvey P. Dale, Aug 25 2015 *)
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PROG
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(Magma) [n eq 1 select 1 else 4*n-Self(n-1)-6: n in [1..70]]; // Vincenzo Librandi, Sep 16 2013
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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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