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A127212
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a(n) = 5^n*Lucas(n), where Lucas = A000204.
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10
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5, 75, 500, 4375, 34375, 281250, 2265625, 18359375, 148437500, 1201171875, 9716796875, 78613281250, 635986328125, 5145263671875, 41625976562500, 336761474609375, 2724456787109375, 22041320800781250, 178318023681640625
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history;
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OFFSET
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1,1
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,25).
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FORMULA
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a(n) = Trace of matrix [({5,5},{5,0})^n].
a(n) = 5^n * Trace of matrix [({1,1},{1,0})^n].
From Colin Barker, Sep 02 2013: (Start)
a(n) = 5*a(n-1) + 25*a(n-2).
G.f.: -5*x*(10*x+1)/(25*x^2+5*x-1). (End)
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MATHEMATICA
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Table[5^n Tr[MatrixPower[{{1, 1}, {1, 0}}, x]], {x, 1, 20}]
Table[5^n*LucasL[n], {n, 1, 50}] (* G. C. Greubel, Dec 18 2017 *)
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PROG
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(PARI) x='x+O('x^30); Vec(-5*x*(10*x+1)/(25*x^2+5*x-1)) \\ G. C. Greubel, Dec 18 2017
(Magma) [5^n*Lucas(n): n in [1..30]]; // G. C. Greubel, Dec 18 2017
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CROSSREFS
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Cf. A000204, A087131, A127210, A127211, A127213, A127214, A127215, A127216.
Sequence in context: A030991 A216093 A151752 * A091903 A105490 A307823
Adjacent sequences: A127209 A127210 A127211 * A127213 A127214 A127215
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KEYWORD
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nonn,easy
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AUTHOR
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Artur Jasinski, Jan 09 2007
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STATUS
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approved
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