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A168301 a(n) = (6*n + 3*(-1)^n - 1)/2.

%I A168301 #23 Sep 08 2022 08:45:49
%S A168301 1,7,7,13,13,19,19,25,25,31,31,37,37,43,43,49,49,55,55,61,61,67,67,73,
%T A168301 73,79,79,85,85,91,91,97,97,103,103,109,109,115,115,121,121,127,127,
%U A168301 133,133,139,139,145,145,151,151,157,157,163,163,169,169,175,175,181,181
%N A168301 a(n) = (6*n + 3*(-1)^n - 1)/2.
%H A168301 Vincenzo Librandi, <a href="/A168301/b168301.txt">Table of n, a(n) for n = 1..1000</a>
%H A168301 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A168301 a(n) = 6*n - a(n-1) - 4, with n>1, a(1)=1.
%F A168301 From _Vincenzo Librandi_, Sep 17 2013: (Start)
%F A168301 G.f.: x*(1 + 6*x - x^2)/((1+x)*(1-x)^2).
%F A168301 a(n) = A168286(n) - 1 = A168328(n) + 1.
%F A168301 a(n) = a(n-1) +a(n-2) -a(n-3). (End)
%F A168301 E.g.f.: (1/2)*(3 - 2*exp(x) + (6*x - 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 17 2016
%t A168301 Table[3 n + 3 (-1)^n/2 - 1/2, {n, 70}] (* _Bruno Berselli_, Sep 17 2013 *)
%t A168301 CoefficientList[Series[(1 + 6 x - x^2)/((1 + x) (1 - x)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 17 2013 *)
%o A168301 (Magma) [n eq 1 select 1 else 6*n-Self(n-1)-4: n in [1..70]]; // _Vincenzo Librandi_, Sep 17 2013
%Y A168301 Cf. A016921, A168328, A168286.
%K A168301 nonn,easy
%O A168301 1,2
%A A168301 _Vincenzo Librandi_, Nov 22 2009
%E A168301 New definition by _Bruno Berselli_, Sep 17 2013