OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..275
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
FORMULA
a(n) = F(n+8) - F(8) with F(n) the Fibonacci numbers A000045.
a(n) = a(n-1) + a(n-2) + 21 for n>1, a(0)=0, a(1)=13, and where 21 = F(8).
G.f.: x*(13 + 8*x)/((1 - x)*(1 - x - x^2)). - Ilya Gutkovskiy, Feb 24 2017
From Colin Barker, Feb 24 2017: (Start)
a(n) = (-21 + (2^(-1-n)*((1-sqrt(5))^n*(-47+21*sqrt(5)) + (1+sqrt(5))^n*(47+21*sqrt(5)))) / sqrt(5)).
a(n) = 2*a(n-1) - a(n-3) for n>2. (End)
MAPLE
nmax:=40: with(combinat): for n from 0 to nmax do a(n):=fibonacci(n+8)-fibonacci(8) od: seq(a(n), n=0..nmax);
MATHEMATICA
Fibonacci[8 +Range[0, 40]] -21 (* G. C. Greubel, Jul 13 2019 *)
PROG
(Magma) [Fibonacci(n+8) - Fibonacci(8): n in [0..40]]; // Vincenzo Librandi, Apr 24 2011
(PARI) concat(0, Vec(x*(13+8*x)/((1-x)*(1-x-x^2)) + O(x^40))) \\ Colin Barker, Feb 24 2017
(PARI) a(n)=fibonacci(n+8)-21 \\ Charles R Greathouse IV, Feb 24 2017
(SageMath) [fibonacci(n+8)-21 for n in (0..40)] # G. C. Greubel, Jul 13 2019
(GAP) List([0..40], n-> Fibonacci(n+8)-21) # G. C. Greubel, Jul 13 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Johannes W. Meijer, Sep 21 2010
STATUS
approved