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A106565 a(n) = 5*a(n-1) + 5*a(n-2) with a(0) = 0, a(1) = 5.

%I A106565 #31 Apr 21 2023 06:15:37
%S A106565 0,5,25,150,875,5125,30000,175625,1028125,6018750,35234375,206265625,
%T A106565 1207500000,7068828125,41381640625,242252343750,1418169921875,
%U A106565 8302111328125,48601406250000,284517587890625,1665594970703125
%N A106565 a(n) = 5*a(n-1) + 5*a(n-2) with a(0) = 0, a(1) = 5.
%H A106565 G. C. Greubel, <a href="/A106565/b106565.txt">Table of n, a(n) for n = 0..1000</a>
%H A106565 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A106565 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,5).
%F A106565 Equals 5*A057088(n). - _T. D. Noe_, Feb 17 2006
%F A106565 From _Philippe Deléham_, Nov 19 2008: (Start)
%F A106565 a(n) = 5*a(n-1) + 5*a(n-2), n > 1; a(0)=0, a(1)=5.
%F A106565 G.f.: 5*x/(1-5*x-5*x^2). (End)
%F A106565 a(n) = (1/6)*5^((n+1)/2)*((1-(-1)^n)*Lucas(2*n) + (1+(-1)^n)*sqrt(5)*Fibonacci(2*n)). - _G. C. Greubel_, Sep 06 2021
%t A106565 LinearRecurrence[{5,5}, {0,5}, 40] (* _G. C. Greubel_, Sep 06 2021 *)
%o A106565 (Magma) I:=[0,5]; [n le 2 select I[n] else 5*(Self(n-1) +Self(n-2)): n in [1..41]]; // _G. C. Greubel_, Sep 06 2021
%o A106565 (Sage) [5*lucas_number1(n, 5, -5) for n in (0..40)] # _G. C. Greubel_, Sep 06 2021
%Y A106565 Cf. A057088.
%K A106565 nonn,easy
%O A106565 0,2
%A A106565 _Roger L. Bagula_, May 30 2005
%E A106565 Name changed by _G. C. Greubel_, Sep 06 2021