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(5*F(n)+3*L(n)-8)/2.
2

%I #22 Jun 13 2015 00:54:10

%S 0,3,7,14,25,43,72,119,195,318,517,839,1360,2203,3567,5774,9345,15123,

%T 24472,39599,64075,103678,167757,271439,439200,710643,1149847,1860494,

%U 3010345,4870843,7881192,12752039,20633235,33385278,54018517,87403799,141422320

%N (5*F(n)+3*L(n)-8)/2.

%D Thomas Koshy, Fibonacci and Lucas Numbers and Applications. Wiley, New York, (2001)

%H Vincenzo Librandi, <a href="/A206417/b206417.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).

%F a(n) = 2*a(n-1)-a(n-3). G.f.: x^2*(x+3) / ((x-1)*(x^2+x-1)). - _Colin Barker_, Oct 28 2014

%t Table[(5*Fibonacci[n] + 3*LucasL[n] - 8)/2, {n, 60}] (* or *) Table[LucasL[n+2] - 4, {n, 60}]

%o (PARI) a(n)=fibonacci(n)+3*fibonacci(n+1)-4 \\ _Charles R Greathouse IV_, Feb 08 2012

%o (PARI) concat(0, Vec(x^2*(x+3)/((x-1)*(x^2+x-1)) + O(x^100))) \\ _Colin Barker_, Oct 28 2014

%Y Cf. A000032, A000045.

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Feb 07 2012

%E Name shortened, _Joerg Arndt_, Oct 28 2014