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A127212 a(n) = 5^n*Lucas(n), where Lucas = A000204. 10
5, 75, 500, 4375, 34375, 281250, 2265625, 18359375, 148437500, 1201171875, 9716796875, 78613281250, 635986328125, 5145263671875, 41625976562500, 336761474609375, 2724456787109375, 22041320800781250, 178318023681640625 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
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)
MATHEMATICA
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 *)
LinearRecurrence[{5, 25}, {5, 75}, 20] (* Harvey P. Dale, Jan 11 2024 *)
PROG
(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
CROSSREFS
Sequence in context: A030991 A216093 A151752 * A091903 A105490 A307823
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Jan 09 2007
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)