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A006483 a(n) = Fibonacci(n)*2^n + 1.

%I A006483 M2502 #40 Oct 01 2022 16:19:05
%S A006483 1,3,5,17,49,161,513,1665,5377,17409,56321,182273,589825,1908737,
%T A006483 6176769,19988481,64684033,209321985,677380097,2192048129,7093616641,
%U A006483 22955425793,74285318145,240392339457,777925951489,2517421260801,8146546327553,26362777698305
%N A006483 a(n) = Fibonacci(n)*2^n + 1.
%D A006483 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006483 Vincenzo Librandi, <a href="/A006483/b006483.txt">Table of n, a(n) for n = 0..1000</a>
%H A006483 D. S. Kluk and N. J. A. Sloane, <a href="/A002050/a002050_3.pdf">Correspondence, 1979</a>.
%H A006483 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A006483 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A006483 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,2,-4).
%F A006483 G.f.: -(-1+6*x^2)/((1-x)*(1-2*x-4*x^2)).
%p A006483 A006483:=-(-1+6*z**2)/(z-1)/(4*z**2+2*z-1); # _Simon Plouffe_ in his 1992 dissertation
%t A006483 lst={};Do[AppendTo[lst, Fibonacci[n]*2^n+1], {n, 0, 5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 19 2008 *)
%t A006483 CoefficientList[Series[(-(- 1 + 6 x^2)) / ((1 - x) (1 - 2 x - 4 x^2)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 09 2013 *)
%t A006483 LinearRecurrence[{3,2,-4},{1,3,5},40] (* _Harvey P. Dale_, Aug 01 2021 *)
%o A006483 (Magma) [Fibonacci(n)*2^n + 1: n in [0..50]]; // _Vincenzo Librandi_, Jun 09 2013
%Y A006483 Cf. A000045, A063727, A087206.
%Y A006483 Equals A103435 + 1.
%K A006483 nonn,easy
%O A006483 0,2
%A A006483 Dennis S. Kluk (mathemagician(AT)ameritech.net)
%E A006483 G.f. in Formula field corrected by _Vincenzo Librandi_, Jun 09 2013