A093136 Expansion of (1 - 8*x)/(1 - 10*x).

1, 2, 20, 200, 2000, 20000, 200000, 2000000, 20000000, 200000000, 2000000000, 20000000000, 200000000000, 2000000000000, 20000000000000, 200000000000000, 2000000000000000, 20000000000000000, 200000000000000000, 2000000000000000000, 20000000000000000000

Offset: 0

Author

Paul Barry, Mar 24 2004

Keywords

• easy
• nonn

Comments

A convex combination of 10^n and 0^n.

Inverse binomial transform of A083294. - Stefano Spezia, Jul 07 2021

Links

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

Crossrefs

Partial sums are A093135.

Cf. A083294, A132026.

Programs

Mathematica

CoefficientList[Series[(1-8x)/(1-10x),{x,0,30}],x] (* or *) LinearRecurrence[{10},{1,2},30] (* Harvey P. Dale, Oct 02 2022 *)

PARI

Vec((1-8*x)/(1-10*x) + O(x^20)) \\ Felix Fröhlich, Jul 07 2021

Formula

a(n) = (2*10^n + 8*0^n)/10.

a(n) = 2*10^(n-1), n > 0. - Vincenzo Librandi, Aug 02 2010

E.g.f.: (8 + 2*exp(10*x))/10. - Stefano Spezia, Jul 05 2021

From Amiram Eldar, May 08 2023: (Start)

Sum_{n>=0} 1/a(n) = 14/9.

Sum_{n>=0} (-1)^n/a(n) = 6/11.

Product_{n>=1} (1 - 1/a(n)) = A132026. (End)