%I #15 Jul 08 2022 08:23:34
%S 1,1,1,3,3,5,9,13,21,35,55,89,145,233,377,611,987,1597,2585,4181,6765,
%T 10947,17711,28657,46369,75025,121393,196419,317811,514229,832041,
%U 1346269,2178309,3524579,5702887,9227465,14930353,24157817,39088169
%N a(n) = 1 + Fibonacci(n) - (Fibonacci(n) mod 2).
%C All-odd Fibonacci sequence.
%H G. C. Greubel, <a href="/A104220/b104220.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,-1,-1).
%F G.f.: (1-x^2-x^4)/((1-x)*(1-x-x^2)*(1+x+x^2)). [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
%F a(n) = (1 + 3*Fibonacci(n) + 2*(-1)^n*ChebyshevT(n, 1/2))/3. - _G. C. Greubel_, Jul 07 2022
%t Table[1+Fibonacci[n] -Mod[Fibonacci[n], 2], {n,0,60}]
%o (Magma) [Fibonacci(n) -(Fibonacci(n) mod 2) +1: n in [0..50]]; // _G. C. Greubel_, Jul 07 2022
%o (SageMath) [fibonacci(n) - (fibonacci(n)%2) + 1 for n in (0..50)] # _G. C. Greubel_, Jul 07 2022
%Y Cf. A000045.
%K nonn
%O 0,4
%A _Roger L. Bagula_, Mar 14 2005