A163664 a(n) = 10^(2*n) + 10^n.

110, 10100, 1001000, 100010000, 10000100000, 1000001000000, 100000010000000, 10000000100000000, 1000000001000000000, 100000000010000000000, 10000000000100000000000, 1000000000001000000000000, 100000000000010000000000000, 10000000000000100000000000000

Offset: 1

Author

Jaroslav Krizek, Aug 02 2009

Keywords

• nonn
• base
• easy

Comments

A161168(n) or A063376(n) for n >= 1 written in base 2.

The digits from the left to the right: a 1, (n-1) times 0, a 1, and n times 0.

Links

• Index entries for linear recurrences with constant coefficients, signature (110,-1000).

Programs

Mathematica

LinearRecurrence[{110,-1000}, {110,10100}, 50] (* G. C. Greubel, Aug 01 2017 *)

PARI

x='x+O('x^50); Vec(10*x*(11 -200*x)/((100*x-1)*(10*x-1))) \\ G. C. Greubel, Aug 01 2017

Formula

a(n) = 110*a(n-1) - 1000*a(n-2).

a(n) = 10*A163449(n).

G.f.: 10*x*(11 -200*x)/((100*x-1)*(10*x-1)).

E.g.f.: exp(100*x) + exp(10*x) -2. - G. C. Greubel, Aug 01 2017

Extensions

Edited by R. J. Mathar, Aug 06 2009