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A190871
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a(n) = 11*a(n-1) - 11*a(n-2), a(0)=0, a(1)=1.
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6
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0, 1, 11, 110, 1089, 10769, 106480, 1052821, 10409751, 102926230, 1017681269, 10062305429, 99490865760, 983714163641, 9726456276691, 96170163243550, 950880776635449, 9401816747310889, 92960295677429840, 919143268231308461, 9088012698092664831
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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) = ((11+sqrt(77))^n-(11-sqrt(77))^n)/(2^n*sqrt(77)).
E.g.f.: (2/sqrt(77))*exp(11*x/2)*sinh(sqrt(77)*x/2). - G. C. Greubel, Dec 18 2015
a(n) = (sqrt(11))^(n-1)*chebyshev_U(n-1, sqrt(11)/2). - G. C. Greubel, Sep 11 2023
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MATHEMATICA
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LinearRecurrence[{11, -11}, {0, 1}, 50] (* T. D. Noe, May 23 2011 *)
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PROG
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(PARI) concat(0, Vec(x/(1-11*x+11*x^2) + O(x^100))) \\ Altug Alkan, Dec 18 2015
(Magma) [n le 2 select n-1 else 11*(Self(n-1) - Self(n-2)): n in [1..31]]; // G. C. Greubel, Sep 11 2023
(SageMath)
def A190871(n): return (sqrt(11))^(n-1)*chebyshev_U(n-1, sqrt(11)/2)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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