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A083336 a(n)=4a(n-2)-a(n-4). 2

%I

%S 3,3,9,12,33,45,123,168,459,627,1713,2340,6393,8733,23859,32592,89043,

%T 121635,332313,453948,1240209,1694157,4628523,6322680,17273883,

%U 23596563,64467009,88063572,240594153,328657725,897909603

%N a(n)=4a(n-2)-a(n-4).

%C a(n)/A002531(n+1) converges to sqrt(3). a(2n)=A082841(n). a(2n)=a(2n-1)+ 3*A002531(2n). a(2n+1)=(1/2)(a(2n)+3*A002531(2n+1)).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 4, 0, -1).

%F G.f.: (3+3x-3x^2)/(1-4x^2+x^4)

%t CoefficientList[Series[(3+3x-3x^2)/(1-4x^2+x^4), {x, 0, 30}], x]

%t Transpose[NestList[Flatten[{Rest[#],4#[[3]]-First[#]}]&, {3,3,9,12}, 50]][[1]] (* _Harvey P. Dale_, Mar 26 2011 *)

%t LinearRecurrence[{0, 4, 0, -1}, {3, 3, 9, 12}, 30] (* _T. D. Noe_, Mar 26 2011 *)

%K easy,nonn

%O 0,1

%A Mario Catalani (mario.catalani(AT)unito.it), Apr 26 2003

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)