OFFSET
0,2
COMMENTS
Generalized Pellian with second term of 8.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (4,1).
FORMULA
a(n) = ((6+sqrt(5))*(2+sqrt(5))^n - (6-sqrt(5))*(2-sqrt(5))^n )/(2*sqrt(5)).
G.f.: (1+4*x)/(1-4*x-x^2). - Philippe Deléham, Nov 03 2008
a(n)=4*a(n-1) + a(n-2); a(0)=1, a(1)=8.
MAPLE
with(combinat): a:=n->4*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008
MATHEMATICA
CoefficientList[Series[(1+4x)/(1-4x-x^2), {x, 0, 20}], x] (* Harvey P. Dale, Mar 30 2011 *)
LinearRecurrence[{4, 1}, {1, 8}, 30] (* Harvey P. Dale, Nov 03 2013 *)
PROG
(Haskell)
a048877 n = a048877_list !! n
a048877_list = 1 : 8 : zipWith (+) a048877_list (map (* 4) $ tail a048877_list)
-- Reinhard Zumkeller, May 01 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved