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Expansion of (1-4*x+3*x^2)/((1-2*x)*(1-4*x+x^2)).
6

%I #15 Mar 15 2023 14:10:53

%S 1,2,6,20,70,252,922,3404,12630,46988,175066,652764,2434966,9085052,

%T 33901146,126511340,472127830,1761967212,6575675482,24540603644,

%U 91586476950,341804779868,1275631593946,4760719498764,17767242206806

%N Expansion of (1-4*x+3*x^2)/((1-2*x)*(1-4*x+x^2)).

%C Binomial transform of A052948.

%H Vincenzo Librandi, <a href="/A087944/b087944.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 (6,-9,2).

%F a(0)=1, a(2)=2, a(2)=6, a(n) = 6*a(n-1)-9*a(n-2)+2*a(n-3), n>2.

%F a(n) = (2^n+(2+sqrt(3))^n+(2-sqrt(3))^n)/3.

%t CoefficientList[Series[(1-4x+3x^2)/((1-2x)(1-4x+x^2)),{x,0,30}],x] (* or *) LinearRecurrence[{6,-9,2},{1,2,6},30] (* _Harvey P. Dale_, Feb 09 2013 *)

%Y Cf. A052948.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Sep 16 2003