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A168286
a(n) = (6*n + 3*(-1)^n + 1)/2.
2
2, 8, 8, 14, 14, 20, 20, 26, 26, 32, 32, 38, 38, 44, 44, 50, 50, 56, 56, 62, 62, 68, 68, 74, 74, 80, 80, 86, 86, 92, 92, 98, 98, 104, 104, 110, 110, 116, 116, 122, 122, 128, 128, 134, 134, 140, 140, 146, 146, 152, 152, 158, 158, 164, 164, 170, 170, 176, 176, 182, 182
OFFSET
1,1
FORMULA
a(n) = 6*n - a(n-1) - 2, with n>1, a(1)=2.
From Vincenzo Librandi, Sep 17 2013: (Start)
a(n) = a(n-1) +a(n-2) -a(n-3).
G.f.: 2*x*(1 + 3*x - x^2)/((1+x)*(1-x)^2).
a(n) = 2*A168233(n) = A168301(n) + 1. (End)
E.g.f.: (1/2)*(3 - 4*exp(x) + (6*x + 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 17 2016
MATHEMATICA
Table[3 n + 3 (-1)^n/2 + 1/2, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)
CoefficientList[Series[(2 + 6 x - 2 x^2)/((1 + x) (1 - x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *)
PROG
(Magma) [n le 1 select n+1 else 6*n-Self(n-1)-2: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Vincenzo Librandi, Nov 22 2009
EXTENSIONS
New definition by Bruno Berselli, Sep 17 2013
STATUS
approved