A134494 a(n) = Fibonacci(6n+2).

1, 21, 377, 6765, 121393, 2178309, 39088169, 701408733, 12586269025, 225851433717, 4052739537881, 72723460248141, 1304969544928657, 23416728348467685, 420196140727489673, 7540113804746346429, 135301852344706746049, 2427893228399975082453

Offset: 0

Author

Artur Jasinski, Oct 28 2007

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..750
• Index entries for linear recurrences with constant coefficients, signature (18,-1).
• Index entries for sequences related to Chebyshev polynomials.

Crossrefs

Cf. A000045, A001906, A001519, A015448, A014445, A033887-A033891, A049310, A049660, A099100, A102312, A103134, A134490 - A134504.

Programs

Magma

[Fibonacci(6*n +2): n in [0..100]]; // Vincenzo Librandi, Apr 17 2011

Maple

seq( combinat[fibonacci](6*n+2),n=0..10) ; # R. J. Mathar, Apr 17 2011

Mathematica

Table[Fibonacci[6n+2], {n, 0, 30}]
Table[ChebyshevU[3*n, 3/2], {n, 0, 20}] (* Vaclav Kotesovec, May 27 2023 *)

PARI

a(n)=fibonacci(6*n+2) \\ Charles R Greathouse IV, Jun 11 2015

PARI

Vec((1+3*x)/(1-18*x+x^2) + O(x^100)) \\ Altug Alkan, Jan 24 2016

Formula

From R. J. Mathar, Jul 04 2011: (Start)

G.f.: ( 1+3*x ) / ( 1-18*x+x^2 ).

a(n) = 3*A049660(n)+A049660(n+1). (End)

a(n) = A000045(A016933(n)). - Michel Marcus, Nov 07 2013

a(n) = ((5-3*sqrt(5)+(5+3*sqrt(5))*(9+4*sqrt(5))^(2*n)))/(10*(9+4*sqrt(5))^n). - Colin Barker, Jan 24 2016

a(n) = S(3*n, 3) = S(n,18) + 3*S(n-1,18), with the Chebyshev S polynomials (A049310), S(-1, x) = 0, and S(n, 18) = A049660(n+1). - Wolfdieter Lang, May 08 2023

Extensions

Index in definition corrected by T. D. Noe, Joerg Arndt, Apr 17 2011