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A104220
a(n) = 1 + Fibonacci(n) - (Fibonacci(n) mod 2).
1
1, 1, 1, 3, 3, 5, 9, 13, 21, 35, 55, 89, 145, 233, 377, 611, 987, 1597, 2585, 4181, 6765, 10947, 17711, 28657, 46369, 75025, 121393, 196419, 317811, 514229, 832041, 1346269, 2178309, 3524579, 5702887, 9227465, 14930353, 24157817, 39088169
OFFSET
0,4
COMMENTS
All-odd Fibonacci sequence.
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
Cf. A000045.
Sequence in context: A245143 A350393 A325849 * A321986 A325187 A209083
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Mar 14 2005
STATUS
approved