A104220 a(n) = 1 + Fibonacci(n) - (Fibonacci(n) mod 2).

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.

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

Cf. A000045.

Sequence in context: A245143 A350393 A325849 * A321986 A325187 A209083

Adjacent sequences: A104217 A104218 A104219 * A104221 A104222 A104223

Keyword

nonn

Author

Roger L. Bagula, Mar 14 2005

Status

approved