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%I #26 Sep 08 2022 08:45:49
%S 2,9,9,16,16,23,23,30,30,37,37,44,44,51,51,58,58,65,65,72,72,79,79,86,
%T 86,93,93,100,100,107,107,114,114,121,121,128,128,135,135,142,142,149,
%U 149,156,156,163,163,170,170,177,177,184,184,191,191,198,198,205,205
%N a(n) = (14*n + 7*(-1)^n + 1)/4.
%H Vincenzo Librandi, <a href="/A168333/b168333.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 a(n) = 7*n - a(n-1) - 3, with n>1, a(1)=2.
%F G.f.: x*(2 + 7*x - 2*x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 17 2013
%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 17 2013
%F a(n) = A168331(n) - 1 = A168337(n) + 1 = A168212(n) - 2 = A168374(n) + 2. - _Bruno Berselli_, Sep 17 2013
%F E.g.f.: (1/4)*(7 - 8*exp(x) + (14*x + 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 18 2016
%t CoefficientList[Series[(2 + 7 x - 2 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 17 2013 *)
%t LinearRecurrence[{1,1,-1},{2,9,9},70] (* _Harvey P. Dale_, Mar 13 2014 *)
%o (Magma) [n eq 1 select 2 else 7*n-Self(n-1)-3: n in [1..70]]; // _Vincenzo Librandi_, Sep 17 2013
%Y Cf. A017005, A168212, A168331, A168337, A168374.
%K nonn,easy,less
%O 1,1
%A _Vincenzo Librandi_, Nov 23 2009
%E New definition by _Bruno Berselli_, Sep 17 2013
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