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
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