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%I #32 Sep 08 2022 08:44:49
%S 1,11,51,176,530,1490,4043,10773,28445,74770,196116,513876,1345861,
%T 3524111,9226935,24157220,63245318,165579398,433493615,1134902265,
%U 2971214081,7778740966,20365009896,53316289896,139583861065,365435294675,956722024443,2504730780248
%N a(n) = T(2n+1, n+2), T given by A027935.
%H Vincenzo Librandi, <a href="/A027942/b027942.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,13,-6,1).
%F a(n) = Fibonacci(2*n+5) - 2*n^2 - 5*n - 5.
%F G.f.: x*(1+5*x-2*x^2)/((1-x)^3*(1-3*x+x^2)). - _Colin Barker_, Sep 20 2012
%p with(combinat): seq(fibonacci(2*n+5) -(2*n^2+5*n+5), n=1..40); # _G. C. Greubel_, Sep 28 2019
%t CoefficientList[Series[(1+5x-2x^2)/((1-x)^3*(1-3x+x^2)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 18 2013 *)
%t LinearRecurrence[{6,-13,13,-6,1},{1,11,51,176,530},40] (* _Harvey P. Dale_, Aug 18 2017 *)
%o (Magma) [Fibonacci(2*n+5)-2*n^2-5*n-5: n in [1..30]]; // _Vincenzo Librandi_, Apr 18 2011
%o (PARI) vector(40, n, fibonacci(2*n+5) -(2*n^2+5*n+5) ) \\ _G. C. Greubel_, Sep 28 2019
%o (Sage) [fibonacci(2*n+5) -(2*n^2+5*n+5) for n in (1..40)] # _G. C. Greubel_, Sep 28 2019
%o (GAP) List([1..40], n-> Fibonacci(2*n+5) -(2*n^2+5*n+5) ); # _G. C. Greubel_, Sep 28 2019
%Y Cf. A000045, A027935.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_
%E More terms from _Vincenzo Librandi_, Oct 18 2013
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