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Expansion of (1-6*x)/(1-10*x).
5

%I #24 Aug 23 2024 08:42:21

%S 1,4,40,400,4000,40000,400000,4000000,40000000,400000000,4000000000,

%T 40000000000,400000000000,4000000000000,40000000000000,

%U 400000000000000,4000000000000000,40000000000000000,400000000000000000,4000000000000000000,40000000000000000000,400000000000000000000

%N Expansion of (1-6*x)/(1-10*x).

%C Partial sums are A093140. A convex combination of 10^n and 0^n.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).

%F a(n) = 4*10^n/10 + 6*0^n/10.

%F a(n) = phi(10^n). - _Paul Barry_, Jul 02 2007

%F a(n) = 4*10^(n-1), n > 0. - _Vincenzo Librandi_, Aug 02 2010

%F From _Elmo R. Oliveira_, Aug 21 2024: (Start)

%F E.g.f.: (2*exp(10*x) + 3)/5.

%F a(n) = 10*a(n-1) for n > 1. (End)

%t Table[EulerPhi[10^n],{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 10 2009 *)

%t Join[{1},NestList[10#&,4,20]] (* _Harvey P. Dale_, Apr 01 2018 *)

%o (PARI) Vec((1-6*x)/(1-10*x) + O(x^30)) \\ _Michel Marcus_, Jan 17 2015

%Y Cf. A093140.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 24 2004

%E a(19)-a(21) from _Elmo R. Oliveira_, Aug 21 2024