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%I #8 Aug 21 2021 10:59:20
%S 1,4,14,50,182,670,2482,9226,34358,128078,477698,1782202,6650086,
%T 24816094,92610194,345616490,1289839382,4813708270,17964928162,
%U 67045873306,250218302918,933826814078,3485087904818,13006522708042
%N Expansion of (1-2x-x^2)/((1-2x)(1-4x+x^2)).
%C First differences of A087944. Binomial transform of A052948(n+1). a(n)=(2/3)A001834+2^n/3.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,2).
%F a(0)=1, a(2)=4, a(2)=14, a(n)=6a(n-1)-9a(n-2)+2a(n-3), n>2; a(n)=(2^n+(1-sqrt(3))(2-sqrt(3))^n+(1+sqrt(3))(2+sqrt(3))^n)/3.
%t CoefficientList[Series[(1-2x-x^2)/((1-2x)(1-4x+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{6,-9,2},{1,4,14},30] (* _Harvey P. Dale_, Aug 21 2021 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Sep 16 2003
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