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A048697 Generalized Pellian with second term equal to 10.

%I A048697 #29 Jun 13 2015 00:50:00
%S A048697 1,10,21,52,125,302,729,1760,4249,10258,24765,59788,144341,348470,
%T A048697 841281,2031032,4903345,11837722,28578789,68995300,166569389,
%U A048697 402134078,970837545,2343809168,5658455881
%N A048697 Generalized Pellian with second term equal to 10.
%H A048697 Reinhard Zumkeller, <a href="/A048697/b048697.txt">Table of n, a(n) for n = 0..1000</a>
%H A048697 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A048697 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,1).
%F A048697 a(n) = 2*a(n-1) + a(n-2); a(0)=1, a(1)=10.
%F A048697 a(n) = ((9+sqrt(2))(1+sqrt(2))^n - (9-sqrt(2))(1-sqrt(2))^n) / 2*sqrt(2).
%F A048697 G.f.: (1+8*x)/(1 - 2*x - x^2). - _Philippe Deléham_, Nov 03 2008
%p A048697 with(combinat): a:=n->8*fibonacci(n-1,2)+fibonacci(n,2): seq(a(n), n=1..25); # _Zerinvary Lajos_, Apr 04 2008
%t A048697 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 *)
%t A048697 LinearRecurrence[{2,1},{1,10},35] (* _Harvey P. Dale_, Jul 26 2011 *)
%o A048697 (Haskell)
%o A048697 a048697 n = a048697_list !! n
%o A048697 a048697_list = 1 : 10 : zipWith (+)
%o A048697                         a048697_list (map (* 2) $ tail a048697_list)
%o A048697 -- _Reinhard Zumkeller_, Sep 05 2014
%Y A048697 Cf. A001333, A000129, A048654, A048655.
%K A048697 easy,nonn
%O A048697 0,2
%A A048697 _Barry E. Williams_