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%I #24 Jan 03 2016 13:24:22
%S 1,9,37,157,665,2817,11933,50549,214129,907065,3842389,16276621,
%T 68948873,292072113,1237237325,5241021413,22201322977,94046313321,
%U 398386576261,1687592618365,7148757049721,30282620817249
%N Generalized Pellian with second term of 9.
%H Harry J. Smith, <a href="/A048878/b048878.txt">Table of n, a(n) for n = 0..1584</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,1).
%F a(n) = ( (7+sqrt(5))(2+sqrt(5))^n - (7-sqrt(5))(2-sqrt(5))^n )/2*sqrt(5).
%F G.f.: (1+5*x)/(1-4*x-x^2). [_Philippe Deléham_, Nov 03 2008]
%e a(n) = 4a(n-1) + a(n-2); a(0)=1, a(1)=9.
%p with(combinat): a:=n->5*fibonacci(n-1,4)+fibonacci(n,4): seq(a(n), n=1..16); # _Zerinvary Lajos_, Apr 04 2008
%t LinearRecurrence[{4,1},{1,9},31] (* or *) CoefficientList[ Series[ (1+5x)/(1-4x-x^2),{x,0,30}],x] (* _Harvey P. Dale_, Jul 12 2011 *)
%o (PARI) { default(realprecision, 2000); for (n=0, 2000, a=round(((7+sqrt(5))*(2+sqrt(5))^n - (7-sqrt(5))*(2-sqrt(5))^n )/10*sqrt(5)); if (a > 10^(10^3 - 6), break); write("b048878.txt", n, " ", a); ); } \\ _Harry J. Smith_, May 31 2009
%Y Cf. A015448, A001077, A001076, A033887.
%K easy,nice,nonn
%O 0,2
%A _Barry E. Williams_
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