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A303427 Interleaved Lucas and Fibonacci numbers.

%I A303427 #27 Sep 08 2022 08:46:21
%S A303427 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 A303427 144,521,233,843,377,1364,610,2207,987,3571,1597,5778,2584,9349,4181,
%U A303427 15127,6765,24476,10946,39603,17711,64079,28657,103682,46368,167761
%N A303427 Interleaved Lucas and Fibonacci numbers.
%H A303427 Harvey P. Dale, <a href="/A303427/b303427.txt">Table of n, a(n) for n = 0..1000</a>
%H A303427 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1).
%F A303427 a(n) = a(n-2) + a(n-4).
%F A303427 G.f.: -(x+1)*(x^2-2*x+2)/(x^4+x^2-1). - _Alois P. Heinz_, Apr 23 2018
%e A303427 a(8) = Lucas(4) = 7;
%e A303427 a(9) = Fibonacci(4) = 3.
%p A303427 a:= n-> (<<0|1>, <1|1>>^iquo(n, 2, 'r'). <<2*(1-r), 1>>)[1, 1]:
%p A303427 seq(a(n), n=0..60);  # _Alois P. Heinz_, Apr 23 2018
%t A303427 LinearRecurrence[{0, 1, 0, 1}, {2, 0, 1, 1}, 60] (* _Vincenzo Librandi_, Apr 25 2018 *)
%t A303427 With[{nn=30},Riffle[LucasL[Range[0,nn]],Fibonacci[Range[0,nn]]]] (* _Harvey P. Dale_, Feb 25 2021 *)
%o A303427 (MATLAB)
%o A303427 F = zeros(1,N);
%o A303427 L = ones(1,N);
%o A303427 F(2) = 1;
%o A303427 L(1) = 2
%o A303427 for  n = 3:N
%o A303427     F(n) = F(n-1) + F(n-2);
%o A303427     L(n) = L(n-1) + L(n-2);
%o A303427 end
%o A303427 A = F;
%o A303427 B = L;
%o A303427 C=[B; A];
%o A303427 C=C(:)';
%o A303427 C
%o A303427 (Magma) [IsEven(n) select Lucas(n div 2) else Fibonacci((n-1) div 2): n in [0..70]]; // _Vincenzo Librandi_, Apr 25 2018
%o A303427 (PARI) a(n) = if(n%2, fibonacci(n\2), fibonacci(n/2-1)+fibonacci(n/2+1)); \\ _Altug Alkan_, Apr 25 2018
%Y A303427 Cf. A000045, A000032, A302126.
%K A303427 nonn,easy
%O A303427 0,1
%A A303427 _Craig P. White_, Apr 23 2018