(Translated by https://www.hiragana.jp/)
A048697 - OEIS
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A048697
Generalized Pellian with second term equal to 10.
3
1, 10, 21, 52, 125, 302, 729, 1760, 4249, 10258, 24765, 59788, 144341, 348470, 841281, 2031032, 4903345, 11837722, 28578789, 68995300, 166569389, 402134078, 970837545, 2343809168, 5658455881
OFFSET
0,2
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
STATUS
approved