A163450 A028403 written in base 2.

100, 1100, 101000, 10010000, 1000100000, 100001000000, 10000010000000, 1000000100000000, 100000001000000000, 10000000010000000000, 1000000000100000000000, 100000000001000000000000, 10000000000010000000000000, 1000000000000100000000000000

Offset: 1

Author

Jaroslav Krizek, Jul 27 2009

Keywords

• nonn
• easy
• base

Comments

The digit pattern is (for n>1): one 1, (n-2) times 0, one 1, and n times 0.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250
• Index entries for linear recurrences with constant coefficients, signature (110,-1000).

Crossrefs

Cf. A007088, A028403.

Programs

Magma

[100] cat [10^(2*n-1)+10^n: n in [2..20]]; // Vincenzo Librandi, Dec 24 2016

Mathematica

Join[{100}, LinearRecurrence[{110, -1000}, {1100, 101000}, 50]] (* or *) Join[{100}, Table[10^(2n-1) + 10^n, {n,1,25}]] (* G. C. Greubel, Dec 24 2016 *)

PARI

Vec(100*x*(1 - 99*x + 800*x^2)/((-1 + 10*x)*(-1 + 100*x)) + O(x^50)) \\ G. C. Greubel, Dec 24 2016

Formula

a(n) = 10^(2n-1) + 10^n, for n >= 2.

a(n) = 110*a(n-1) -1000*a(n-2), n>3.

G.f.: 100*x*(1 - 99*x + 800*x^2) / ((-1 + 10*x)*(-1 + 100*x)). - G. C. Greubel, Dec 24 2016

a(n) = A007088(A028403(n)). - Michel Marcus, Dec 24 2016

Extensions

Recurrence added by R. J. Mathar, Oct 21 2009