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%I #7 May 02 2022 03:03:58
%S 3,2,8,14,40,92,236,576,1440,3560,8848,21936,54448,135072,335168,
%T 831584,2063360,5119552,12702656,31517696,78201600,194033280,
%U 481434368,1194532096,2963866368,7353928192
%N a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) with a(0)=3, a(1)=2, a(3)=8.
%H G. C. Greubel, <a href="/A107300/b107300.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2).
%F G.f.: (3-4*x-2*x^2)/(1-2*x-2*x^2+2*x^3). [Sep 28 2009]
%F a(n) = 3*A077937(n) - 4*A077937(n-1) - 2*A077937(n-2). [Sep 28 2009]
%F a(n) = 2*(b1^n + b2^n + b3^n)/(b1 + b2 + b3), where b1, b2, and b3 and the roots of x^3 = 2*x^2 + 2*x - 2.
%t LinearRecurrence[{2,2,-2}, {3,2,8}, 46]
%o (Magma) I:=[3,2,8]; [n le 3 select I[n] else 2*(Self(n-1) +Self(n-2) -Self(n-3)): n in [1..46]]; // _G. C. Greubel_, May 02 2022
%o (SageMath)
%o def A107300_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( (3-4*x-2*x^2)/(1-2*x-2*x^2+2*x^3) ).list()
%o A107300_list(45) # _G. C. Greubel_, May 02 2022
%Y Cf. A077937.
%K nonn,easy
%O 0,1
%A _Roger L. Bagula_, May 20 2005
%E Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
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