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%I #32 Mar 04 2024 01:12:12
%S 2,10,8,16,14,22,20,28,26,34,32,40,38,46,44,52,50,58,56,64,62,70,68,
%T 76,74,82,80,88,86,94,92,100,98,106,104,112,110,118,116,124,122,130,
%U 128,136,134,142,140,148,146,154,152,160,158,166,164,172,170,178,176,184
%N a(n) = 6*n - a(n-1), with n>1, a(1)=2.
%H Vincenzo Librandi, <a href="/A166542/b166542.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F G.f.: -x*(-2-8*x+4*x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 13 2013
%F From _G. C. Greubel_, May 16 2016: (Start)
%F E.g.f.: (1/2)*(3*(1 + 2*x)*exp(x) + 5*exp(-x) - 8).
%F a(n) = a(n-1) + a(n-2) - a(n-3). (End)
%F a(n) = 2*A166517(n). - _Philippe Deléham_, Nov 29 2016
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 1/4 + Pi/(6*sqrt(3)). - _Amiram Eldar_, Feb 23 2023
%t CoefficientList[Series[-(- 2 - 8 x + 4 x^2)/((1 + x) (x - 1)^2), {x, 0, 80}], x] (* _Vincenzo Librandi_, Sep 13 2013 *)
%t LinearRecurrence[{1,1,-1}, {2, 10, 8}, 50] (* _G. C. Greubel_, May 16 2016 *)
%o (Magma) [n eq 1 select 2 else 6*n-Self(n-1): n in [1..80]]; // _Vincenzo Librandi_, Sep 13 2013
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Oct 16 2009
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