%I #27 Sep 08 2022 08:46:21

%S 2,0,1,1,3,1,4,2,7,3,11,5,18,8,29,13,47,21,76,34,123,55,199,89,322,

%T 144,521,233,843,377,1364,610,2207,987,3571,1597,5778,2584,9349,4181,

%U 15127,6765,24476,10946,39603,17711,64079,28657,103682,46368,167761

%N Interleaved Lucas and Fibonacci numbers.

%H Harvey P. Dale, <a href="/A303427/b303427.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 (0,1,0,1).

%F a(n) = a(n-2) + a(n-4).

%F G.f.: -(x+1)*(x^2-2*x+2)/(x^4+x^2-1). - _Alois P. Heinz_, Apr 23 2018

%e a(8) = Lucas(4) = 7;

%e a(9) = Fibonacci(4) = 3.

%p a:= n-> (<<0|1>, <1|1>>^iquo(n, 2, 'r'). <<2*(1-r), 1>>)[1, 1]:

%p seq(a(n), n=0..60); # _Alois P. Heinz_, Apr 23 2018

%t LinearRecurrence[{0, 1, 0, 1}, {2, 0, 1, 1}, 60] (* _Vincenzo Librandi_, Apr 25 2018 *)

%t With[{nn=30},Riffle[LucasL[Range[0,nn]],Fibonacci[Range[0,nn]]]] (* _Harvey P. Dale_, Feb 25 2021 *)

%o (MATLAB)

%o F = zeros(1,N);

%o L = ones(1,N);

%o F(2) = 1;

%o L(1) = 2

%o for n = 3:N

%o F(n) = F(n-1) + F(n-2);

%o L(n) = L(n-1) + L(n-2);

%o end

%o A = F;

%o B = L;

%o C=[B; A];

%o C=C(:)';

%o C

%o (Magma) [IsEven(n) select Lucas(n div 2) else Fibonacci((n-1) div 2): n in [0..70]]; // _Vincenzo Librandi_, Apr 25 2018

%o (PARI) a(n) = if(n%2, fibonacci(n\2), fibonacci(n/2-1)+fibonacci(n/2+1)); \\ _Altug Alkan_, Apr 25 2018

%Y Cf. A000045, A000032, A302126.

%K nonn,easy

%O 0,1

%A _Craig P. White_, Apr 23 2018