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%I #16 Sep 08 2022 08:44:49
%S 1,8,26,73,196,518,1361,3568,9346,24473,64076,167758,439201,1149848,
%T 3010346,7881193,20633236,54018518,141422321,370248448,969323026,
%U 2537720633,6643838876,17393795998,45537549121,119218851368,312119004986,817138163593,2139295485796
%N a(n) = T(2*n+1,n+1), T given by A026998.
%H Colin Barker, <a href="/A027004/b027004.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 (4,-4,1).
%F a(n) = Fibonacci(2*n+3) + 2*Fibonacci(2*n+2) - 3.
%F From _Colin Barker_, Feb 18 2016: (Start)
%F a(n) = 2^(-n)*(-3*2^n-(3-sqrt(5))^n*(-2+sqrt(5))+(2+sqrt(5))*(3+sqrt(5))^n).
%F a(n) = 4*a(n-1)-4*a(n-2)+a(n-3) for n>2.
%F G.f.: (1+4*x-2*x^2) / ((1-x)*(1-3*x+x^2)).
%F (End)
%o (Magma) [Fibonacci(2*n+3) + 2*Fibonacci(2*n+2) - 3: n in [0..30]]; // _Vincenzo Librandi_, Apr 18 2011
%o (PARI) Vec((1+4*x-2*x^2)/((1-x)*(1-3*x+x^2)) + O(x^40)) \\ _Colin Barker_, Feb 18 2016
%Y A002878(n+1) - 3.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_