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 (4,1)
FORMULA
a(n) = ((8+sqrt(5))*(2+sqrt(5))^n - (8-sqrt(5))*(2-sqrt(5))^n)2*sqrt(5).
From Philippe Deléham, Nov 03 2008: (Start)
a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=10.
G.f.: (1+6*x)/(1-4*x-x^2). (End)
For n >= 1, a(n) equals the denominator of the continued fraction [4, 4, ..., 4, 10] (with n copies of 4). The numerator of that continued fraction is a(n+1). - ZhenShu Luan, Aug 05 2019
MAPLE
with(combinat): a:=n->6*fibonacci(n-1, 4)+fibonacci(n, 4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008
MATHEMATICA
LinearRecurrence[{4, 1}, {1, 10}, 30] (* Harvey P. Dale, Jul 18 2011 *)
PROG
(Haskell)
a048879 n = a048879_list !! n
a048879_list = 1 : 10 : zipWith (+)
a048879_list (map (* 4) $ tail a048879_list)
-- Reinhard Zumkeller, Mar 03 2014
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Jul 18 2011
STATUS
approved