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A106565
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a(n) = 5*a(n-1) + 5*a(n-2) with a(0) = 0, a(1) = 5.
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3
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0, 5, 25, 150, 875, 5125, 30000, 175625, 1028125, 6018750, 35234375, 206265625, 1207500000, 7068828125, 41381640625, 242252343750, 1418169921875, 8302111328125, 48601406250000, 284517587890625, 1665594970703125
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 5*a(n-1) + 5*a(n-2), n > 1; a(0)=0, a(1)=5.
G.f.: 5*x/(1-5*x-5*x^2). (End)
a(n) = (1/6)*5^((n+1)/2)*((1-(-1)^n)*Lucas(2*n) + (1+(-1)^n)*sqrt(5)*Fibonacci(2*n)). - G. C. Greubel, Sep 06 2021
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MATHEMATICA
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LinearRecurrence[{5, 5}, {0, 5}, 40] (* G. C. Greubel, Sep 06 2021 *)
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PROG
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(Magma) I:=[0, 5]; [n le 2 select I[n] else 5*(Self(n-1) +Self(n-2)): n in [1..41]]; // G. C. Greubel, Sep 06 2021
(Sage) [5*lucas_number1(n, 5, -5) for n in (0..40)] # G. C. Greubel, Sep 06 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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