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A163309
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a(n) = 18*a(n-1) - 76*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
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3
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1, 10, 104, 1112, 12112, 133504, 1482560, 16539776, 185041408, 2073722368, 23263855616, 261146501120, 2932583993344, 32939377795072, 370032416817152, 4157190790283264, 46706970546995200, 524778969784385536
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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(5))*(9+sqrt(5))^n + (5-sqrt(5))*(9-sqrt(5))^n)/10.
G.f.: (1-8*x)/(1-18*x+76*x^2).
E.g.f.: (1/5)*exp(9*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016
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MATHEMATICA
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LinearRecurrence[{18, -76}, {1, 10}, 50] (* G. C. Greubel, Dec 18 2016 *)
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PROG
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(Magma) [ n le 2 select 9*n-8 else 18*Self(n-1)-76*Self(n-2): n in [1..18] ];
(PARI) Vec((1-8*x)/(1-18*x+76*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 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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