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a(n) = (F(4*n) - F(n))/2, where F=A000045 (the Fibonacci sequence).
1

%I #10 Sep 08 2022 08:44:58

%S 0,1,10,71,492,3380,23180,158899,1089144,7465159,51167050,350704322,

%T 2403763416,16475639933,112925716670,774004377655,5305104928368,

%U 36361730123272,249227005938340,1708227311451263

%N a(n) = (F(4*n) - F(n))/2, where F=A000045 (the Fibonacci sequence).

%H G. C. Greubel, <a href="/A049672/b049672.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7,-6,1).

%F G.f.: x*(-1-2*x+2*x^2) / ( (x^2+x-1)*(x^2-7*x+1) ). - _R. J. Mathar_, Oct 26 2015

%t LinearRecurrence[{8, -7, -6, 1}, {0, 1, 10, 71}, 50] (* or *) Table[(1/2) *(Fibonacci[4*n] - Fibonacci[n]), {n,0,30}] (* _G. C. Greubel_, Dec 02 2017 *)

%o (PARI) for(n=0,30, print1((fibonacci(4*n) - fibonacci(n))/2, ", ")) \\ _G. C. Greubel_, Dec 02 2017

%o (Magma) [(Fibonacci(4*n) - Fibonacci(n))/2: n in [0..30]]; // _G. C. Greubel_, Dec 02 2017

%K nonn,easy

%O 0,3

%A _Clark Kimberling_