A006483 a(n) = Fibonacci(n)*2^n + 1. (Formerly M2502)

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

0,2

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).

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000045, A063727, A087206.

Equals A103435 + 1.

Sequence in context: A106063 A215106 A368651 * A177960 A271659 A357442

Adjacent sequences: A006480 A006481 A006482 * A006484 A006485 A006486

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved