OFFSET
0,2
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 (2,1).
FORMULA
a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=10.
a(n) = ((9+sqrt(2))(1+sqrt(2))^n - (9-sqrt(2))(1-sqrt(2))^n) / 2*sqrt(2).
G.f.: (1+8*x)/(1 - 2*x - x^2). - Philippe Deléham, Nov 03 2008
MAPLE
with(combinat): a:=n->8*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..25); # Zerinvary Lajos, Apr 04 2008
MATHEMATICA
a[n_]:=(MatrixPower[{{1, 2}, {1, 1}}, n].{{9}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2010 *)
LinearRecurrence[{2, 1}, {1, 10}, 35] (* Harvey P. Dale, Jul 26 2011 *)
PROG
(Haskell)
a048697 n = a048697_list !! n
a048697_list = 1 : 10 : zipWith (+)
a048697_list (map (* 2) $ tail a048697_list)
-- Reinhard Zumkeller, Sep 05 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved