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A084131
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a(n) = 10*a(n-1) - 17*a(n-2), a(0) = 1, a(1) = 5.
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2
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1, 5, 33, 245, 1889, 14725, 115137, 901045, 7053121, 55213445, 432231393, 3383685365, 26488919969, 207366548485, 1623353845377, 12708307129525, 99486055923841, 778819338036485, 6096930429659553, 47729375549975285
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (5+sqrt(8))^n/2 + (5-sqrt(8))^n/2.
G.f.: (1-5*x)/(1-10*x+17*x^2).
E.g.f.: exp(5*x)*cosh(sqrt(8)*x).
a(n) = 17^((n-1)/2)*( sqrt(17)*ChebyshevU(n, 5/sqrt(17)) - 5*ChebyshevU(n-1, 5/sqrt(17)) ). - G. C. Greubel, Oct 13 2022
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MATHEMATICA
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LinearRecurrence[{10, -17}, {1, 5}, 20] (* Harvey P. Dale, Apr 04 2021 *)
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PROG
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(Magma) [n le 2 select 5^(n-1) else 10*Self(n-1) -17*Self(n-2): n in [1..41]]; // G. C. Greubel, Oct 13 2022
(SageMath)
A084131=BinaryRecurrenceSequence(10, -17, 1, 5)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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