A022384 - OEIS

%I #22 Sep 08 2022 08:44:46

%S 4,18,22,40,62,102,164,266,430,696,1126,1822,2948,4770,7718,12488,

%T 20206,32694,52900,85594,138494,224088,362582,586670,949252,1535922,

%U 2485174,4021096,6506270,10527366,17033636,27561002,44594638,72155640,116750278,188905918,305656196

%N Fibonacci sequence beginning 4, 18.

%H G. C. Greubel, <a href="/A022384/b022384.txt">Table of n, a(n) for n = 0..1000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1).

%F G.f.: (4+14*x)/(1-x-x^2). - _Philippe Deléham_, Nov 19 2008

%F a(0)=4, a(1)=18, a(n) = a(n-1) + a(n-2). - _Harvey P. Dale_, Sep 04 2011

%F a(n) = 4*Fibonacci(n+2) + 10*Fibonacci(n) = 4*Fibonacci(n+2) + 18*Fibonacci(n). - _G. C. Greubel_, Mar 02 2018

%t LinearRecurrence[{1,1},{4,18},40] (* or *) CoefficientList[ Series[ -((2 (7x+2))/(x^2+x-1)),{x,0,40}],x](* _Harvey P. Dale_, Sep 04 2011 *)

%t Table[4*Fibonacci[n+2] + 10*Fibonacci[n], {n,0,50}] (* _G. C. Greubel_, Mar 02 2018 *)

%o (PARI) for(n=0, 50, print1(4*fibonacci(n+2) + 10*fibonacci(n), ", ")) \\ _G. C. Greubel_, Mar 02 2018

%o (Magma) [4*Fibonacci(n+2) + 10*Fibonacci(n): n in [0..50]]; // _G. C. Greubel_, Mar 02 2018

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E Terms a(30) onward added by _G. C. Greubel_, Mar 02 2018