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A190977
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a(n) = 8*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
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3
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0, 1, 8, 59, 432, 3161, 23128, 169219, 1238112, 9058801, 66279848, 484944779, 3548158992, 25960548041, 189943589368, 1389745974739, 10168249851072, 74397268934881, 544336902223688, 3982708873115099, 29139986473802352, 213206347424843321, 1559950847029734808
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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(11))^n - (4 - sqrt(11))^n)/(2*sqrt(11)). - Giorgio Balzarotti, May 28 2011
a(n) = 5^((n-1)/2)*ChebyshevU(n-1, 4/sqrt(5)).
E.g.f.: (1/sqrt(11))*exp(4*x)*sinh(sqrt(11)*x). (End)
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MATHEMATICA
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LinearRecurrence[{8, -5}, {0, 1}, 50]
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PROG
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(Magma) [n le 2 select n-1 else 8*Self(n-1) -5*Self(n-2): n in [1..41]]; // G. C. Greubel, Jun 17 2022
(SageMath) [sum( (-1)^k*binomial(n-k-1, k)*5^k*8^(n-2*k-1) for k in (0..((n-1)//2))) for n in (0..40)] # G. C. Greubel, Jun 17 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
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AUTHOR
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STATUS
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approved
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