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a(0)=2, a(1)=2, a(n) = 2*a(n-1) + 10*a(n-2).
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%I #23 Feb 26 2024 01:58:34

%S 2,2,24,68,376,1432,6624,27568,121376,518432,2250624,9685568,41877376,

%T 180610432,779994624,3366093568,14532133376,62725202432,270771738624,

%U 1168795501568,5045308389376

%N a(0)=2, a(1)=2, a(n) = 2*a(n-1) + 10*a(n-2).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, 10).

%F G.f.: (2*(x-1))/(2*x(5*x+1)-1). - _Harvey P. Dale_, Oct 15 2013

%p a[0]:=2:a[1]:=2:for i from 2 to 40 do a[i]:=2*a[i-1]+10*a[i-2] od: seq(a[n],n=0..40);

%t LinearRecurrence[{2,10},{2,2},30] (* or *) CoefficientList[Series[(2*(x-1))/(2*x(5*x+1)-1),{x,0,30}],x] (* _Harvey P. Dale_, Oct 15 2013 *)

%o (Sage) [lucas_number2(n,2,-10) for n in range(0, 21)] # _Zerinvary Lajos_, Apr 30 2009

%K easy,nonn

%O 0,1

%A _Miklos Kristof_, Mar 27 2007