A134495 a(n) = Fibonacci(6n + 3).

2, 34, 610, 10946, 196418, 3524578, 63245986, 1134903170, 20365011074, 365435296162, 6557470319842, 117669030460994, 2111485077978050, 37889062373143906, 679891637638612258, 12200160415121876738

Offset: 0

Author

Artur Jasinski, Oct 28 2007

Keywords

• nonn
• easy

Comments

From Tanya Khovanova, Jan 06 2023: (Start)

Fibonacci(6n+3) are divisible by 2 but not by 4.

These numbers are not divisible by 3. (End)

Links

• Index entries for linear recurrences with constant coefficients, signature (18,-1).
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Cf. A000045, 2*A007805, A049660, A134492, A134493, A134494, A103134.

Subsequence of A091999.

Programs

Magma

[Fibonacci(6*n +3): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011

Mathematica

Table[Fibonacci[6n+3], {n, 0, 30}]
LinearRecurrence[{18,-1},{2,34},20] (* Harvey P. Dale, Jul 28 2018 *)

PARI

a(n)=fibonacci(6*n+3) \\ Charles R Greathouse IV, Jun 11 2015

Formula

From R. J. Mathar, Apr 17 2011: (Start)

G.f.: (2-2*x) / (1 - 18*x + x^2).

a(n) = 2*A007805(n). (End)

a(n) = A000045(A016945(n)). - Michel Marcus, Nov 08 2013

a(n) = 2*(S(n, 18) - S(n-1, 18)), n >= 0, with the Chebyshev S-polynomials S(n-1, 18) = A049660(n). (See the g.f.) - Wolfdieter Lang, Jul 10 2018

Extensions

Index in definition and offset corrected by R. J. Mathar, Apr 17 2011