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A134495
a(n) = Fibonacci(6n + 3).
11
2, 34, 610, 10946, 196418, 3524578, 63245986, 1134903170, 20365011074, 365435296162, 6557470319842, 117669030460994, 2111485077978050, 37889062373143906, 679891637638612258, 12200160415121876738
OFFSET
0,1
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)
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
MATHEMATICA
Table[Fibonacci[6n+3], {n, 0, 30}]
LinearRecurrence[{18, -1}, {2, 34}, 20] (* Harvey P. Dale, Jul 28 2018 *)
PROG
(Magma) [Fibonacci(6*n +3): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011
(PARI) a(n)=fibonacci(6*n+3) \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
Subsequence of A091999.
Sequence in context: A119298 A045585 A092883 * A173208 A344107 A361773
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Oct 28 2007
EXTENSIONS
Index in definition and offset corrected by R. J. Mathar, Apr 17 2011
STATUS
approved