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

1, 3, 5, 17, 49, 161, 513, 1665, 5377, 17409, 56321, 182273, 589825, 1908737, 6176769, 19988481, 64684033, 209321985, 677380097, 2192048129, 7093616641, 22955425793, 74285318145, 240392339457, 777925951489, 2517421260801, 8146546327553, 26362777698305

Offset: 0

Author

Dennis S. Kluk (mathemagician(AT)ameritech.net)

Keywords

• nonn
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• D. S. Kluk and N. J. A. Sloane, Correspondence, 1979.
• Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
• Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
• Index entries for linear recurrences with constant coefficients, signature (3,2,-4).

Crossrefs

Cf. A000045, A063727, A087206.

Equals A103435 + 1.

Programs

Magma

[Fibonacci(n)*2^n + 1: n in [0..50]]; // Vincenzo Librandi, Jun 09 2013

Maple

A006483:=-(-1+6*z**2)/(z-1)/(4*z**2+2*z-1); # Simon Plouffe in his 1992 dissertation

Mathematica

lst={};Do[AppendTo[lst, Fibonacci[n]*2^n+1], {n, 0, 5!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 19 2008 *)
CoefficientList[Series[(-(- 1 + 6 x^2)) / ((1 - x) (1 - 2 x - 4 x^2)), {x, 0, 50}], x] (* Vincenzo Librandi, Jun 09 2013 *)
LinearRecurrence[{3,2,-4},{1,3,5},40] (* Harvey P. Dale, Aug 01 2021 *)

Formula

G.f.: -(-1+6*x^2)/((1-x)*(1-2*x-4*x^2)).

Extensions

G.f. in Formula field corrected by Vincenzo Librandi, Jun 09 2013