A048879 Generalized Pellian with second term of 10.
1, 10, 41, 174, 737, 3122, 13225, 56022, 237313, 1005274, 4258409, 18038910, 76414049, 323695106, 1371194473, 5808472998, 24605086465, 104228818858, 441520361897, 1870310266446, 7922761427681, 33561355977170, 142168185336361, 602234097322614
Offset: 0
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)
Programs
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Haskell
a048879 n = a048879_list !! n a048879_list = 1 : 10 : zipWith (+) a048879_list (map (* 4) $ tail a048879_list) -- Reinhard Zumkeller, Mar 03 2014 -
Maple
with(combinat): a:=n->6*fibonacci(n-1,4)+fibonacci(n,4): seq(a(n), n=1..16); # Zerinvary Lajos, Apr 04 2008
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Mathematica
LinearRecurrence[{4,1},{1,10},30] (* Harvey P. Dale, Jul 18 2011 *)
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
Extensions
More terms from Harvey P. Dale, Jul 18 2011