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%I #24 Sep 08 2022 08:45:47
%S 10,17,31,59,115,227,451,899,1795,3587,7171,14339,28675,57347,114691,
%T 229379,458755,917507,1835011,3670019,7340035,14680067,29360131,
%U 58720259,117440515,234881027,469762051,939524099,1879048195,3758096387
%N a(n) = 7*2^n + 3.
%C Contains the primes 17, 31, 59, 227, 57347, 114691, 14680067, 7516192771,..
%H Vincenzo Librandi, <a href="/A164285/b164285.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F a(n) = 2*a(n-1) - 3.
%F a(n) = 3*a(n-1) - 2*a(n-2).
%F a(n) = A005009(n) + 3, a(0)=10.
%F G.f.: (10-13*x)/((2*x-1)*(x-1)).
%F E.g.f.: 7*exp(2*x) + 3*exp(x). - _G. C. Greubel_, Sep 12 2017
%e At n=0, a(0)=7*2^0+3=10. At n=1, a(1)=7*2^1+3=17.
%t CoefficientList[Series[(10 - 13 x) / ((2 x - 1) (x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Sep 12 2013 *)
%t LinearRecurrence[{3,-2},{10,17},40] (* _Harvey P. Dale_, Aug 29 2017 *)
%o (Magma) [7*2^n+3: n in [0..40]]; // _Vincenzo Librandi_, Sep 12 2013
%o (PARI) x='x+O('x^50); Vec((10-13*x)/((2*x-1)*(x-1))) \\ _G. C. Greubel_, Sep 12 2017
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Aug 12 2009
%E Offset corrected by _R. J. Mathar_, Aug 19 2009