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%I #8 Sep 08 2022 08:45:46
%S 3,20,140,1000,7200,52000,376000,2720000,19680000,142400000,
%T 1030400000,7456000000,53952000000,390400000000,2824960000000,
%U 20441600000000,147916800000000,1070336000000000,7745024000000000,56043520000000000
%N a(n) = ((3+sqrt(5))*(5+sqrt(5))^n + (3-sqrt(5))*(5-sqrt(5))^n)/2.
%C Binomial transform of A163064. Fifth binomial transform of A163114.
%C 10^(floor(n/2)) | a(n). - _G. C. Greubel_, Dec 22 2017
%H G. C. Greubel, <a href="/A163065/b163065.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-20).
%F a(n) = 10*a(n-1) - 20*a(n-2) for n > 1; a(0) = 3, a(1) = 20.
%F G.f.: (3-10*x)/(1-10*x+20*x^2).
%t CoefficientList[Series[(3-10*x)/(1-10*x+20*x^2), {x,0,50}], x] (* or *) LinearRecurrence[{10,-20}, {3,20}, 30] (* _G. C. Greubel_, Dec 22 2017 *)
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((3+r)*(5+r)^n+(3-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 21 2009
%o (Magma) I:=[3,20]; [n le 2 select I[n] else 10*Self(n-1) - 20*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Dec 22 2017
%o (PARI) x='x+O('x^30); Vec((3-10*x)/(1-10*x+20*x^2)) \\ _G. C. Greubel_, Dec 22 2017
%Y Cf. A163064, A163114.
%K nonn
%O 0,1
%A Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 21 2009
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