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Expansion of (1+4x-6x^2-36x^3)/(1-19x^2+90x^4).
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%I #8 Dec 24 2022 12:42:46

%S 1,4,13,40,157,400,1813,4000,20317,40000,222853,400000,2405677,

%T 4000000,25651093,40000000,270859837,400000000,2837738533,4000000000,

%U 29539646797,40000000000,305856821173,400000000000,3152711390557

%N Expansion of (1+4x-6x^2-36x^3)/(1-19x^2+90x^4).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,19,0,-90).

%F G.f. : 4(1+x)/(1-10x^2)-3/(1-9x^2); a(n)=19a(n-2)-90a(n-4); a(n)=(2+sqrt(10)/5)(sqrt(10))^n+(2-sqrt(10)/5)(-sqrt(10))^n-3^(n+1)(1+(-1)^n)/2; a(n)=sum{k=0..n, binomial(floor(n/2), floor(k/2))3^k }

%t CoefficientList[Series[(1+4x-6x^2-36x^3)/(1-19x^2+90x^4),{x,0,40}],x] (* or *) LinearRecurrence[{0,19,0,-90},{1,4,13,40},40] (* _Harvey P. Dale_, Dec 24 2022 *)

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jul 25 2004