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A272912 Difference sequence of the sequence A116470 of all distinct Fibonacci numbers and Lucas numbers (A000032).

%I A272912 #22 Oct 23 2018 18:48:51
%S A272912 1,1,1,1,2,1,3,2,5,3,8,5,13,8,21,13,34,21,55,34,89,55,144,89,233,144,
%T A272912 377,233,610,377,987,610,1597,987,2584,1597,4181,2584,6765,4181,10946,
%U A272912 6765,17711,10946,28657,17711,46368,28657,75025,46368,121393,75025
%N A272912 Difference sequence of the sequence A116470 of all distinct Fibonacci numbers and Lucas numbers (A000032).
%C A272912 Every term is a Fibonacci number (A000045).
%H A272912 Clark Kimberling, <a href="/A272912/b272912.txt">Table of n, a(n) for n = 1..1000</a>
%H A272912 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1).
%F A272912 From _Colin Barker_, May 10 2016: (Start)
%F A272912 a(n) = a(n-2)+a(n-4) for n>4.
%F A272912 G.f.: x*(1+x-x^5) / (1-x^2-x^4).
%F A272912 (End)
%F A272912 a(n) = A053602(n-2), n>2. - _R. J. Mathar_, May 20 2016
%F A272912 a(n) = A123231(n-3), n>3. - _Georg Fischer_, Oct 23 2018
%e A272912 A116470 = (1, 2, 3, 4, 5, 7, 8, 11, 13, 18, 21, 29, 34, 47, 55, 76,...), so that (a(n)) = (1,1,1,1,2,1,3,2,5,3,8,5,13,8,12,...).
%t A272912 u = Table[Fibonacci[n], {n, 1, 200}]; v = Table[LucasL[n], {n, 1, 200}];
%t A272912 Take[Differences[Union[u, v]], 100]
%o A272912 (PARI) Vec(x*(1+x-x^5)/(1-x^2-x^4) + O(x^50)) \\ _Colin Barker_, May 10 2016
%Y A272912 Cf. A000045, A000032, A116470, A053602, A123231.
%K A272912 nonn,easy
%O A272912 1,5
%A A272912 _Clark Kimberling_, May 10 2016