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A173802
a(n) = (5*10^n - 23)/9.
2
3, 53, 553, 5553, 55553, 555553, 5555553, 55555553, 555555553, 5555555553, 55555555553, 555555555553, 5555555555553, 55555555555553, 555555555555553, 5555555555555553, 55555555555555553, 555555555555555553, 5555555555555555553, 55555555555555555553, 555555555555555555553
OFFSET
1,1
FORMULA
a(n) = 10*a(n-1) + 23 for n > 1.
G.f.: x*(3+20*x)/((10*x-1)*(x-1)). - R. J. Mathar, Aug 24 2011
From Elmo R. Oliveira, Sep 09 2024: (Start)
E.g.f.: exp(x)*(5*exp(9*x) - 23)/9.
a(n) = 11*a(n-1) - 10*a(n-2) for n > 2. (End)
EXAMPLE
For n=2, a(2) = 10*3 + 23 = 53.
For n=3, a(3) = 10*53 + 23 = 553.
For n=4, a(4) = 10*553 + 23 = 5553.
MATHEMATICA
Rest[CoefficientList[Series[x*(3 + 20*x)/((10*x - 1)*(x - 1)), {x, 0, 50}], x]] (* G. C. Greubel, May 06 2017 *)
Table[FromDigits[PadLeft[{3}, n, 5]], {n, 20}] (* or *) LinearRecurrence[ {11, -10}, {3, 53}, 20] (* Harvey P. Dale, May 27 2018 *)
PROG
(PARI) x=x+O('x^50); Vec(x*(3+20*x)/((10*x-1)*(x-1))) \\ G. C. Greubel, May 06 2017
CROSSREFS
Cf. A093164.
Sequence in context: A215435 A121504 A099665 * A001279 A092447 A167217
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 25 2010
STATUS
approved