%I #42 Aug 04 2024 16:30:30
%S 1,19,11,29,21,39,31,49,41,59,51,69,61,79,71,89,81,99,91,109,101,119,
%T 111,129,121,139,131,149,141,159,151,169,161,179,171,189,181,199,191,
%U 209,201,219,211,229,221,239,231,249,241,259,251,269,261,279,271,289
%N a(n) = 10*n - a(n-1), with n>1, a(1)=1.
%H Vincenzo Librandi, <a href="/A166525/b166525.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*(1+18*x-9*x^2) / ( (1+x)*(1-x)^2 ). - _R. J. Mathar_, Mar 08 2011
%F From _G. C. Greubel_, May 16 2016: (Start)
%F E.g.f.: (1/2)*(13*exp(-x) + 5*(1 + 2*x)*exp(x) - 18).
%F a(n) = a(n-1) + a(n-2) - a(n-3). (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 1/9 + sqrt(5+2*sqrt(5))*Pi/10. - _Amiram Eldar_, Feb 24 2023
%F a(n) = (1/2)*(10*n + 5 + 13*(-1)^n). - _G. C. Greubel_, Aug 04 2024
%t CoefficientList[Series[(1 +18 x -9 x^2)/((1+x) (1-x)^2), {x,0,80}], x] (* _Vincenzo Librandi_, Sep 13 2013 *)
%t LinearRecurrence[{1,1,-1}, {1,19,11}, 50] (* _G. C. Greubel_, May 16 2016 *)
%o (Magma) [n eq 1 select 1 else 10*n-Self(n-1): n in [1..80]]; // _Vincenzo Librandi_, Sep 13 2013
%o (SageMath)
%o def A166525(n): return 5*n - 4 + 13*((n+1)%2)
%o [A166525(n) for n in range(1, 101)] # _G. C. Greubel_, Aug 04 2024
%Y Cf. A166519, A166520, A166521, A166522, A166523, A166524, A166526.
%K nonn,easy
%O 1,2
%A _Vincenzo Librandi_, Oct 16 2009