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

%I A134494 #36 May 27 2023 03:53:04
%S A134494 1,21,377,6765,121393,2178309,39088169,701408733,12586269025,
%T A134494 225851433717,4052739537881,72723460248141,1304969544928657,
%U A134494 23416728348467685,420196140727489673,7540113804746346429,135301852344706746049,2427893228399975082453
%N A134494 a(n) = Fibonacci(6n+2).
%H A134494 Colin Barker, <a href="/A134494/b134494.txt">Table of n, a(n) for n = 0..750</a>
%H A134494 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-1).
%H A134494 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%F A134494 From _R. J. Mathar_, Jul 04 2011: (Start)
%F A134494 G.f.: ( 1+3*x ) / ( 1-18*x+x^2 ).
%F A134494 a(n) = 3*A049660(n)+A049660(n+1). (End)
%F A134494 a(n) = A000045(A016933(n)). - _Michel Marcus_, Nov 07 2013
%F A134494 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
%F A134494 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
%p A134494 seq( combinat[fibonacci](6*n+2),n=0..10) ; # _R. J. Mathar_, Apr 17 2011
%t A134494 Table[Fibonacci[6n+2], {n, 0, 30}]
%t A134494 Table[ChebyshevU[3*n, 3/2], {n, 0, 20}] (* _Vaclav Kotesovec_, May 27 2023 *)
%o A134494 (Magma) [Fibonacci(6*n +2): n in [0..100]]; // _Vincenzo Librandi_, Apr 17 2011
%o A134494 (PARI) a(n)=fibonacci(6*n+2) \\ _Charles R Greathouse IV_, Jun 11 2015
%o A134494 (PARI) Vec((1+3*x)/(1-18*x+x^2) + O(x^100)) \\ _Altug Alkan_, Jan 24 2016
%Y A134494 Cf. A000045, A001906, A001519, A015448, A014445, A033887-A033891, A049310, A049660, A099100, A102312, A103134, A134490 - A134504.
%K A134494 nonn,easy
%O A134494 0,2
%A A134494 _Artur Jasinski_, Oct 28 2007
%E A134494 Index in definition corrected by _T. D. Noe_, _Joerg Arndt_, Apr 17 2011