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%I #12 Sep 17 2016 18:37:07
%S 1,5,10,14,28,32,64,68,136,140,280,284,568,572,1144,1148,2296,2300,
%T 4600,4604,9208,9212,18424,18428,36856,36860,73720,73724,147448,
%U 147452,294904,294908,589816,589820,1179640,1179644,2359288,2359292,4718584,4718588,9437176
%N Expansion of (1+5*x+7*x^2-x^3)/((1-2*x^2)*(1-x)*(1+x)).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-2).
%F G.f.: (1+5*x+7*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)).
%F a(n) = a(n-1)+4 if n odd.
%F a(n) = a(n-1)*2 if n even.
%F a(2n) = 9*2^n - 8 = A048491(n).
%F a(2n+1) = 9*2^n - 4 = A053209(n+1).
%F a(n) = 3*a(n-2) - 2*a(n-4) with n>3, a(0)=1, a(1)=5, a(2)=10, a(3)=14.
%F a(n) = 9*2^floor(n/2)-2*(-1)^n-6. [_Bruno Berselli_, Apr 27 2013]
%t CoefficientList[Series[(1+5x+7x^2-x^3)/((1-2x^2)(1-x)(1+x)),{x,0,40}],x] (* or *) LinearRecurrence[{0,3,0,-2},{1,5,10,14},50] (* _Harvey P. Dale_, Sep 17 2016 *)
%Y Cf. A048491, A053209.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Apr 15 2013
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