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A168283
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a(n) = (10*n - 5*(-1)^n - 3)/4.
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2
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3, 3, 8, 8, 13, 13, 18, 18, 23, 23, 28, 28, 33, 33, 38, 38, 43, 43, 48, 48, 53, 53, 58, 58, 63, 63, 68, 68, 73, 73, 78, 78, 83, 83, 88, 88, 93, 93, 98, 98, 103, 103, 108, 108, 113, 113, 118, 118, 123, 123, 128, 128, 133, 133, 138, 138, 143, 143, 148, 148, 153, 153, 158
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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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a(n) = 5*n - a(n-1) - 4, with n>1, a(1)=3.
a(n) = (10*n + 5*(-1)^(n+1) - 3)/4.
G.f.: x*(3 + 2*x^2)/((1+x)*(x-1)^2). (End)
E.g.f.: (1/4)*(-5 + 8*exp(x) + (10*x - 3)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 17 2016
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MATHEMATICA
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CoefficientList[Series[(3 + 2 x^2) / ((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 16 2013 *)
Table[5 n/2 - 5 (-1)^n/4 - 3/4, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)
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PROG
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(Magma) [n le 1 select n+2 else 5*n-Self(n-1)-4: 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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Previous definition replaced with the closed form by Bruno Berselli, Sep 17 2013
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STATUS
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approved
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