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A033889
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Fibonacci(4*n+1).
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9
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1, 5, 34, 233, 1597, 10946, 75025, 514229, 3524578, 24157817, 165580141, 1134903170, 7778742049, 53316291173, 365435296162, 2504730781961, 17167680177565, 117669030460994, 806515533049393, 5527939700884757, 37889062373143906, 259695496911122585, 1779979416004714189
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = A167816(4*n+1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 13 2009]
For positive n, a(n) equals (-1)^n times the permanent of the (4n)X(4n) tridiagonal matrix with sqrt(i)'s along the three central diagonals, where i is the imaginary unit. [From John M. Campbell, Jul 12, 2011]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (7,-1).
Tanya Khovanova, Recursive Sequences
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FORMULA
| a(n)=7*a(n-1)-a(n-2). - Floor van Lamoen (fvlamoen(AT)hotmail.com), Dec 10 2001
O.g.f.: (1-2*x)/(1-7*x+x^2). a(n) = A004187(n+1)-2*A004187(n-1). - R. J. Mathar, Jan 17 2008
a(n)=(1/2)*[7/2-(3/2)*sqrt(5)]^n-(1/10)*[7/2-(3/2)*sqrt(5)]^n*sqrt(5)+(1/10)*sqrt(5)*[7/2+(3/2) *sqrt(5)]^n+(1/2)*[7/2+(3/2)*sqrt(5)]^n, with n>=0 - Paolo P. Lava, Jun 25 2008
a(n) = Fibonacci(4*n+1)=sqrt(1+2*Fibonacci(2*n)* Fibonacci(2*n+1)+5*(Fibonacci(2*n)* Fibonacci(2*n+1))^2) [From Artur Jasinski, Feb 06 2010]
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MATHEMATICA
| Table[Fibonacci[4*n+1], {n, 0, 14}] (Vladimir Orlovsky, Jul 21 2008)
Table[Sqrt[1 + 2 m + 5 m^2] /. m -> Fibonacci[2 n] Fibonacci[2 n + 1], {n, 0, 20}] (* Artur Jasinski, Feb 06 2010 *)
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PROG
| (MAGMA) [Fibonacci(4*n+1): n in [0..100]]; // Vincenzo Librandi, Apr 16 2011
(PARI) a(n)=fibonacci(4*n+1) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Cf. A081018, A081016, A172968. [From Artur Jasinski, Feb 06 2010]
Sequence in context: A024063 A015545 A102436 * A120469 A180909 A183415
Adjacent sequences: A033886 A033887 A033888 * A033890 A033891 A033892
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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