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A190976
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a(n) = 8*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.
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4
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0, 1, 8, 61, 464, 3529, 26840, 204133, 1552544, 11807953, 89805992, 683024077, 5194774640, 39509124889, 300488675192, 2285382026869, 17381590189376, 132196575434401, 1005427832907080, 7646832936953437, 58158379996906256, 442326541164389737
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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) = ((4 + sqrt(13))^n - (4 - sqrt(13))^n)/(2*sqrt(13)). - Giorgio Balzarotti, May 28 2011
a(n) = 3^((n-1)/2)*ChebyshevU(n-1, 4/sqrt(3)).
E.g.f.: (1/sqrt(13))*exp(4*x)*sinh(sqrt(13)*x). (End)
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MATHEMATICA
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LinearRecurrence[{8, -3}, {0, 1}, 50]
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PROG
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(Magma) [n le 2 select n-1 else 8*Self(n-1) - 3*Self(n-2): n in [1..51]]; // G. C. Greubel, Jun 11 2022
(SageMath) [lucas_number1(n, 8, 3) for n in (0..50)] # G. C. Greubel, Jun 11 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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nonn,easy
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AUTHOR
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STATUS
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approved
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