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A163447
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a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
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3
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1, 11, 119, 1273, 13513, 142667, 1500479, 15737929, 164744881, 1722111467, 17983160807, 187650088633, 1957031891641, 20402217047531, 212634387415919, 2215643826731593, 23083472275311073, 240466638643803467
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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) = ((1+sqrt(2))*(9+sqrt(2))^n + (1-sqrt(2))*(9-sqrt(2))^n)/2.
G.f.: (1-7*x)/(1-18*x+79*x^2).
E.g.f.: exp(9*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016
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MATHEMATICA
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LinearRecurrence[{18, -79}, {1, 11}, 50] (* G. C. Greubel, Dec 23 2016 *)
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PROG
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(Magma) [ n le 2 select 10*n-9 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];
(PARI) Vec((1-7*x)/(1-18*x+79*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016
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CROSSREFS
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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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