A126431 a(n) = n * 10^n.

0, 10, 200, 3000, 40000, 500000, 6000000, 70000000, 800000000, 9000000000, 100000000000, 1100000000000, 12000000000000, 130000000000000, 1400000000000000, 15000000000000000, 160000000000000000

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (20,-100).

Formula

a(0)=0, a(1)=10; for n>1, a(n) = 20*a(n-1) - 100*a(n-2). - Harvey P. Dale, Mar 30 2012

G.f.: 10*x/(1 - 10*x)^2. - Vincenzo Librandi, Sep 09 2014

From Amiram Eldar, Jul 20 2020: (Start)

Sum_{n>=1} 1/a(n) = log(10/9).

Sum_{n>=1} (-1)^(n+1)/a(n) = log(11/10). (End)

Maple

A126431 := proc(n) n*10^n ; end proc: # Bruno Berselli, Sep 09 2014

Mathematica

Table[n 10^n, {n, 0, 20}] (* or *) LinearRecurrence[{20, -100}, {0, 10}, 20] (* Harvey P. Dale, Mar 30 2012 *)
CoefficientList[Series[10 x/(1 - 10 x)^2, {x, 0, 20}], x] (* Vincenzo Librandi, Sep 09 2014 *)

Prog

(Magma) [n*10^n: n in [0..20]]; // Vincenzo Librandi, Sep 09 2014
(PARI) a(n)=n*10^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Sequence in context: A079436 A285021 A354410 * A335649 A202436 A320671

Adjacent sequences: A126428 A126429 A126430 * A126432 A126433 A126434

Keyword

nonn,easy

Author

Jonathan R. Love (japanada11(AT)yahoo.ca), Mar 11 2007

Status

approved