A163449 A007582 written in base 2.

1, 11, 1010, 100100, 10001000, 1000010000, 100000100000, 10000001000000, 1000000010000000, 100000000100000000, 10000000001000000000, 1000000000010000000000, 100000000000100000000000, 10000000000001000000000000, 1000000000000010000000000000, 100000000000000100000000000000

Offset

0,2

Comments

For n >= 1, the digits are a "1", (n-1) times "0", a "1", and (n-1) times "0".

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

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

Formula

a(n) = 10^(2*n-1) + 10^(n-1) = A163664(n)/10 for n >= 1.

a(n) = A007088(A007582(n)). - Michel Marcus, Dec 24 2016

From Elmo R. Oliveira, Nov 21 2025: (Start)

G.f.: (1 - 99*x + 800*x^2)/((100*x-1)*(10*x-1)).

E.g.f.: (8 + exp(10*x) + exp(100*x))/10.

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

Mathematica

Join[{1}, Table[10^(2n-1) + 10^(n-1), {n, 1, 25}]] (* or *) Join[{1}, LinearRecurrence[{110, -1000}, {11, 1010}, 25]] (* G. C. Greubel, Dec 24 2016 *)

Prog

(PARI) concat([1], for(n=1, 50, print1(10^(2*n-1) + 10^(n-1), ", "))) \\ G. C. Greubel, Dec 24 2016

Crossrefs

Cf. A007088, A007582.

Sequence in context: A281277 A281176 A280459 * A288900 A288830 A289047

Adjacent sequences: A163446 A163447 A163448 * A163450 A163451 A163452

Keyword

nonn,base,easy

Author

Jaroslav Krizek, Jul 27 2009

Extensions

Edited by R. J. Mathar, Aug 06 2009

Status

approved