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%I #9 Jul 31 2015 12:32:23
%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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