A093141 Expansion of (1-6*x)/(1-10*x).

1, 4, 40, 400, 4000, 40000, 400000, 4000000, 40000000, 400000000, 4000000000, 40000000000, 400000000000, 4000000000000, 40000000000000, 400000000000000, 4000000000000000, 40000000000000000, 400000000000000000, 4000000000000000000, 40000000000000000000, 400000000000000000000

Offset: 0

Author

Paul Barry, Mar 24 2004

Keywords

• easy
• nonn

Comments

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

Links

• Index entries for linear recurrences with constant coefficients, signature (10).

Crossrefs

Cf. A093140.

Programs

Mathematica

Table[EulerPhi[10^n],{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Nov 10 2009 *)
Join[{1},NestList[10#&,4,20]] (* Harvey P. Dale, Apr 01 2018 *)

PARI

Vec((1-6*x)/(1-10*x) + O(x^30)) \\ Michel Marcus, Jan 17 2015

Formula

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

a(n) = phi(10^n). - Paul Barry, Jul 02 2007

a(n) = 4*10^(n-1), n > 0. - Vincenzo Librandi, Aug 02 2010

From Elmo R. Oliveira, Aug 21 2024: (Start)

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

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

Extensions

a(19)-a(21) from Elmo R. Oliveira, Aug 21 2024