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%I #15 Sep 03 2019 02:45:18
%S 1,5,21,85,421,1445,8181,24565,155461,417605,2904981,7099285,53578981,
%T 120687845,977951541,2051693365,17698918021,34878787205,318061475541,
%U 592939382485,5681922991141,10079969502245,100990737360501
%N Expansion of (1 + 5*x - 12*x^2 - 80*x^3)/(1 - 33*x^2 + 272*x^4).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,33,0,-272).
%F G.f.: 5*(1+x)/(1-17*x^2) - 4/(1-16*x^2).
%F a(n) = 33*a(n-2) - 272*a(n-4).
%F a(n) = (5/2 + 5*sqrt(17)/34)*(sqrt(17))^n + (5/2 - 5*sqrt(17)/34)*(-sqrt(17))^n - 4^(n+1)*(1+(-1)^n)/2.
%F a(n) = Sum_{k=0..n} binomial(floor(n/2), floor(k/2))4^k.
%t CoefficientList[Series[(1+5x-12x^2-80x^3)/(1-33x^2+272x^4), {x,0,30}], x] (* or *) LinearRecurrence[{0,33,0,-272},{1,5,21,85},30] (* _Harvey P. Dale_, Jul 19 2011 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Jul 25 2004
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