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%I #35 Feb 17 2023 22:33:26
%S 1,13,144,1597,17711,196418,2178309,24157817,267914296,2971215073,
%T 32951280099,365435296162,4052739537881,44945570212853,
%U 498454011879264,5527939700884757,61305790721611591,679891637638612258
%N a(n) = Fibonacci(5*n + 2).
%C The o.g.f. of {F(m*n + 2)}_{n>=0}, for m = 1, 2, ..., is
%C G(m,x) = (1 + F(m - 2)*x) / (1 - L(m)*x + (-1)^m*x^2), with F = A000045 and F(-1) = 1, and L = A000032. - _Wolfdieter Lang_, Feb 06 2023
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,1).
%F From _R. J. Mathar_, Jul 04 2011: (Start)
%F G.f.: (-1-2*x) / (-1 + 11*x + x^2).
%F a(n) = 2*A049666(n) + A049666(n+1). (End)
%F a(n) = A000045(A016873(n)). - _Michel Marcus_, Nov 05 2013
%t Table[Fibonacci[5n + 2], {n, 0, 30}]
%t LinearRecurrence[{11,1},{1,13},20] (* _Harvey P. Dale_, May 05 2022 *)
%o (Magma) [Fibonacci(5*n+2): n in [0..50]]; // _Vincenzo Librandi_, Apr 20 2011
%Y Cf. A000045, A001906, A001519, A033887, A015448, A014445, A033888-A033891, A102312, A099100, A134490-A134495, A103134, A134497-A134504.
%K nonn,easy
%O 0,2
%A _Artur Jasinski_, Oct 28 2007
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