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%I #31 Jun 13 2015 00:50:00
%S 1,8,33,140,593,2512,10641,45076,190945,808856,3426369,14514332,
%T 61483697,260449120,1103280177,4673569828,19797559489,83863807784,
%U 355252790625,1504874970284,6374752671761
%N a(n) = 4*a(n-1) + a(n-2); a(0)=1, a(1)=8.
%C Generalized Pellian with second term of 8.
%H Reinhard Zumkeller, <a href="/A048877/b048877.txt">Table of n, a(n) for n = 0..1000</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) = ((6+sqrt(5))*(2+sqrt(5))^n - (6-sqrt(5))*(2-sqrt(5))^n )/(2*sqrt(5)).
%F G.f.: (1+4*x)/(1-4*x-x^2). - _Philippe Deléham_, Nov 03 2008
%F a(n)=4*a(n-1) + a(n-2); a(0)=1, a(1)=8.
%p with(combinat): a:=n->4*fibonacci(n-1,4)+fibonacci(n,4): seq(a(n), n=1..16); # _Zerinvary Lajos_, Apr 04 2008
%t CoefficientList[Series[(1+4x)/(1-4x-x^2),{x,0,20}],x] (* _Harvey P. Dale_, Mar 30 2011 *)
%t LinearRecurrence[{4,1},{1,8},30] (* _Harvey P. Dale_, Nov 03 2013 *)
%o (Haskell)
%o a048877 n = a048877_list !! n
%o a048877_list = 1 : 8 : zipWith (+) a048877_list (map (* 4) $ tail a048877_list)
%o -- _Reinhard Zumkeller_, May 01 2013
%Y Cf. A015448, A001076, A001077, A033887.
%K easy,nonn
%O 0,2
%A _Barry E. Williams_
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