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%I #25 Oct 13 2022 16:50:48
%S 1,2,14,68,356,1832,9464,48848,252176,1301792,6720224,34691648,
%T 179087936,924501632,4772534144,24637146368,127183790336,656558039552,
%U 3389334900224,17496687838208,90322760754176,466271170045952
%N a(n) = 4*a(n-1) + 6*a(n-2), a(0)=1, a(1)=2.
%C Binomial transform of A002535.
%H G. C. Greubel, <a href="/A084132/b084132.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 (4,6).
%F a(n) = (2+sqrt(10))^n/2 + (2-sqrt(10))^n/2.
%F G.f.: (1-2*x)/(1-4*x-6*x^2).
%F E.g.f.: exp(2*x)*cosh(sqrt(10)*x).
%F a(n) = Sum_{k=0..n} A201730(n,k)*9^k. - _Philippe Deléham_, Dec 06 2011
%F G.f.: G(0)/2, where G(k) = 1 + 1/(1 - x*(5*k-2)/(x*(5*k+3) - 1/G(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Jun 03 2013
%F a(n) = 2*i^n*6^((n-2)/2)*( 3*ChebyshevU(n, 2/(i*sqrt(6))) + i*sqrt(6)*ChebyshevU(n -1, 2/(i*sqrt(6))) ). - _G. C. Greubel_, Oct 13 2022
%t LinearRecurrence[{4,6}, {1,2}, 40] (* _G. C. Greubel_, Oct 13 2022 *)
%o (SageMath) [lucas_number2(n,4,-6)/2 for n in range(0, 22)] # _Zerinvary Lajos_, May 14 2009
%o (SageMath)
%o A084132=BinaryRecurrenceSequence(4,6,1,2)
%o [A084132(n) for n in range(41)] # _G. C. Greubel_, Oct 13 2022
%o (Magma) [n le 2 select 2^(n-1) else 4*Self(n-1) +6*Self(n-2): n in [1..40]]; // _G. C. Greubel_, Oct 13 2022
%Y Cf. A002535, A005667, A201730.
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 16 2003
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