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%I #35 Jul 18 2022 09:49:42
%S 4,14,18,32,50,82,132,214,346,560,906,1466,2372,3838,6210,10048,16258,
%T 26306,42564,68870,111434,180304,291738,472042,763780,1235822,1999602,
%U 3235424,5235026,8470450,13705476,22175926,35881402,58057328,93938730
%N Fibonacci sequence beginning 4, 14.
%H Harvey P. Dale, <a href="/A022383/b022383.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+10*x)/(1-x-x^2). - _Philippe Deléham_, Nov 19 2008
%F a(n) = 4*Fibonacci(n+2) + 6*Fibonacci(n) = 4*Fibonacci(n) + 14*Fibonacci(n-1). - _G. C. Greubel_, Mar 06 2018
%F E.g.f.: 4*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 6*sqrt(5)*sinh(sqrt(5)*x/2))/5. - _Stefano Spezia_, Jul 17 2022
%F a(n) = 2 * A022113(n). - _Alois P. Heinz_, Jul 17 2022
%t a[1] := 4; a[2] := 14; a[n_] := a[n - 1] + a[n - 2]; Table[a[n], {n, 1, 30}] (* _Stefan Steinerberger_, Apr 08 2006 *)
%t LinearRecurrence[{1,1},{4,14},40] (* _Harvey P. Dale_, Feb 15 2015 *)
%o (PARI) Vec((4+10*x)/(1-x-x^2)+O(x^99)) \\ _Charles R Greathouse IV_, May 15 2013
%o (Magma) [4*Fibonacci(n+2) + 6*Fibonacci(n): n in [0..40]]; // _G. C. Greubel_, Mar 06 2018
%Y Cf. A000045, A022113.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Stefan Steinerberger_, Apr 08 2006
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