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A190971
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a(n) = 5*a(n-1) - 10*a(n-2), with a(0)=0, a(1)=1.
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2
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0, 1, 5, 15, 25, -25, -375, -1625, -4375, -5625, 15625, 134375, 515625, 1234375, 1015625, -7265625, -46484375, -159765625, -333984375, -72265625, 2978515625, 15615234375, 48291015625, 85302734375, -56396484375, -1135009765625, -5111083984375, -14205322265625
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (i/sqrt(15))*(((5 - i*sqrt(15))/2)^n - ((5 + i*sqrt(15))/2)^n). - Giorgio Balzarotti, May 28 2011
a(n) = 10^((n-1)/2) * ChebyshevU(n-1, sqrt(10)/4).
E.g.f.: (2/sqrt(15))*exp(5*x/2)*sin(sqrt(15)*x/2). (End)
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MATHEMATICA
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LinearRecurrence[{5, -10}, {0, 1}, 50]
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PROG
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(PARI) concat(0, Vec(x/(1-5*x+10*x^2) + O(x^100))) \\ Altug Alkan, Nov 26 2015
(Magma) [n le 2 select n-1 else 5*(Self(n-1) - 2*Self(n-2)): n in [1..51]]; // G. C. Greubel, Jun 10 2022
(Sage) [lucas_number1(n, 5, 10) for n in (0..50)] # G. C. Greubel, Jun 10 2022
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CROSSREFS
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Cf. A190958 (index to generalized Fibonacci sequences).
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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