OFFSET
0,4
COMMENTS
All-odd Fibonacci sequence.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1,-1,-1).
FORMULA
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]
a(n) = (1 + 3*Fibonacci(n) + 2*(-1)^n*ChebyshevT(n, 1/2))/3. - G. C. Greubel, Jul 07 2022
MATHEMATICA
Table[1+Fibonacci[n] -Mod[Fibonacci[n], 2], {n, 0, 60}]
PROG
(Magma) [Fibonacci(n) -(Fibonacci(n) mod 2) +1: n in [0..50]]; // G. C. Greubel, Jul 07 2022
(SageMath) [fibonacci(n) - (fibonacci(n)%2) + 1 for n in (0..50)] # G. C. Greubel, Jul 07 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Mar 14 2005
STATUS
approved