A098610 a(n) = 10^n + (-1)^n.

2, 9, 101, 999, 10001, 99999, 1000001, 9999999, 100000001, 999999999, 10000000001, 99999999999, 1000000000001, 9999999999999, 100000000000001, 999999999999999, 10000000000000001, 99999999999999999, 1000000000000000001, 9999999999999999999, 100000000000000000001

Offset: 0

Author

Henry Bottomley, Sep 17 2004

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (9,10).

Crossrefs

Cf. A015585, A094028, A098609, A098611.

Programs

Magma

[10^n+(-1)^n: n in [0..20]]; // Vincenzo Librandi, Sep 23 2016

Mathematica

Total/@Partition[Riffle[10^Range[0,20],{1,-1}],2] (* or *) Table[10^n+(-1)^n,{n,0,20}] (* Harvey P. Dale, Aug 20 2012 *)

Formula

a(n) = A098611(n) + 2*(-1)^n.

a(n) = A098609(n)/A098611(n).

a(n) = A098609(n)/(11*A015585(n)).

a(n) = 9*A094028(n+1)/A015585(n).

From Chai Wah Wu, Sep 22 2016: (Start)

a(n) = 9*a(n-1) + 10*a(n-2) for n > 1.

G.f.: (9*x - 2)/((x + 1)*(10*x - 1)). (End)

E.g.f.: exp(-x)*(exp(11*x) + 1). - Elmo R. Oliveira, Aug 17 2024