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A134493
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a(n) = Fibonacci(6*n+1).
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11
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1, 13, 233, 4181, 75025, 1346269, 24157817, 433494437, 7778742049, 139583862445, 2504730781961, 44945570212853, 806515533049393, 14472334024676221, 259695496911122585, 4660046610375530309, 83621143489848422977, 1500520536206896083277, 26925748508234281076009
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OFFSET
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0,2
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COMMENTS
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For positive n, a(n) equals (-1)^n times the permanent of the (6n)X(6n) tridiagonal matrix with ((-1)^(1/6))'s along the three central diagonals. - John M. Campbell, Jul 12 2011
a(n) = x + y where those two values are solutions to: x^2 = 5*y^2 + 1. (See related sequences with formula below). - Richard R. Forberg, Sep 05 2013
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LINKS
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FORMULA
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G.f.: ( 1-5*x ) / ( 1-18*x+x^2 ).
a(n) = Fibonacci(3*n+1)^2 + Fibonacci(3*n)^2. - Gary Detlefs, Oct 12 2011
a(n) = ((5-sqrt(5)+(5+sqrt(5))*(9+4*sqrt(5))^(2*n)))/(10*(9+4*sqrt(5))^n). - Colin Barker, Jan 24 2016
a(n) = S(n, 18) - 5*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
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MATHEMATICA
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Table[Fibonacci[6n+1], {n, 0, 30}]
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PROG
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(PARI) Vec((1-5*x)/(1-18*x+x^2) + O(x^100)) \\ Altug Alkan, Jan 24 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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