This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A135992 #26 Apr 27 2024 17:21:57
%S A135992 1,1,3,2,8,5,21,13,55,34,144,89,377,233,987,610,2584,1597,6765,4181,
%T A135992 17711,10946,46368,28657,121393,75025,317811,196418,832040,514229,
%U A135992 2178309,1346269,5702887,3524578,14930352,9227465,39088169,24157817
%N A135992 Positive Fibonacci numbers swapped in pairs.
%C A135992 Analogous to A108362. It could be natural to define here too a(0) = 1 (swapping Fibonacci numbers from A212804). - _Giuseppe Coppoletta_, Mar 04 2015
%H A135992 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-1).
%F A135992 From _Emeric Deutsch_, Mar 22 2008: (Start)
%F A135992 a(2n-1) = Fibonacci(2n), a(2n) = Fibonacci(2n-1).
%F A135992 a(2n-1) = a(2n-2) + 2*a(2n-3), a(2n) = a(2n-1) - a(2n-3), a(1)=a(2)=1. (End)
%F A135992 G.f.: (x*(1+x-x^3)) / ((x^2+x-1)*(x^2-x-1)). - _R. J. Mathar_, Mar 08 2011
%F A135992 a(n) = (Lucas(n) - (-1)^n * Fibonacci(n))/2. - _Vladimir Reshetnikov_, Sep 24 2016
%e A135992 a(7) = Fibonacci(8) = 21, a(8) = Fibonacci(7) = 13.
%p A135992 a[1]:=1: a[2]:=1: for n from 2 to 20 do a[2*n-1]:=a[2*n-2]+2*a[2*n-3]: a[2*n]:=a[2*n-1]-a[2*n-3] end do: seq(a[n],n=1..40); # _Emeric Deutsch_, Mar 22 2008
%t A135992 Flatten[{Last[#],First[#]}&/@Partition[Fibonacci[Range[40]],2]] (* _Harvey P. Dale_, Sep 16 2013 *)
%t A135992 Table[(LucasL[n] - (-1)^n Fibonacci[n])/2, {n, 40}] (* _Vladimir Reshetnikov_, Sep 24 2016 *)
%o A135992 (SageMath) [fibonacci(n-(-1)^n) for n in range (1,39)] # _Giuseppe Coppoletta_, Mar 04 2015
%Y A135992 Cf. A000045, A001906, A108362, A212804.
%K A135992 nonn,easy
%O A135992 1,3
%A A135992 _Paul Curtz_, Mar 03 2008
%E A135992 More terms from _Emeric Deutsch_, Mar 22 2008