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

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (9,10).

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

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 *)

Prog

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

Crossrefs

Cf. A015585, A094028, A098609, A098611.

Sequence in context: A378045 A369673 A041239 * A226391 A348858 A125815

Adjacent sequences: A098607 A098608 A098609 * A098611 A098612 A098613

Keyword

easy,nonn

Author

Henry Bottomley, Sep 17 2004

Status

approved