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%I #13 Feb 19 2016 08:37:54
%S 1,6,47,199,661,1954,5442,14696,39065,103025,270655,709716,1859412,
%T 4869594,12750611,33383659,87401977,228824086,599072310,1568395100,
%U 4106115485,10749954101,28143749827,73681298664,192900149736,505019154414,1322157317687
%N a(n) = T(2*n, n+1), T given by A027011.
%H Colin Barker, <a href="/A027012/b027012.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,13,-6,1)
%F a(1)=1, a(n) = Lucas(2*n+6) - (6*n^2+17*n+18). - _Ralf Stephan_, May 05 2005
%F From _Colin Barker_, Feb 19 2016: (Start)
%F a(n) = -8 + (2^(-1-n)*((3-sqrt(5))^n*(-15+7*sqrt(5))+(3+sqrt(5))^n*(15+7*sqrt(5))))/sqrt(5) + 13*(1+n) - 6*(1+n)*(2+n) for n>1.
%F a(n) = 6*a(n-1)-13*a(n-2)+13*a(n-3)-6*a(n-4)+a(n-5) for n>6.
%F G.f.: x*(1+24*x^2-18*x^3+6*x^4-x^5) / ((1-x)^3*(1-3*x+x^2)).
%F (End)
%t Join[{1},LinearRecurrence[{6,-13,13,-6,1},{6,47,199,661,1954},30]] (* _Harvey P. Dale_, Nov 17 2013 *)
%o (PARI) Vec(x*(1+24*x^2-18*x^3+6*x^4-x^5)/((1-x)^3*(1-3*x+x^2)) + O(x^40)) \\ _Colin Barker_, Feb 19 2016
%K nonn,easy
%O 1,2
%A _Clark Kimberling_
%E More terms from _Harvey P. Dale_, Nov 17 2013
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