A094026 Expansion of x(1+10x)/((1-x^2)(1-10x^2)).

0, 1, 10, 11, 110, 111, 1110, 1111, 11110, 11111, 111110, 111111, 1111110, 1111111, 11111110, 11111111, 111111110, 111111111, 1111111110, 1111111111, 11111111110, 11111111111, 111111111110, 111111111111, 1111111111110

Offset: 0

Author

Paul Barry, Apr 22 2004

Keywords

• easy
• nonn

Comments

The expansion of x(1+kx)/((1-x^2)(1-kx^2)) has a(n)=k^((n+1)/2)/(2(sqrt(k)-1))-(-sqrt(k))^(n+1)/(2(sqrt(k)+1))-(-1)^n/2-(k+1)/(2(k-1)).

First 4 positive members are the divisors of 6 (the first perfect number), written in base 2 (see A135652, A135653, A135654, A135655). - Omar E. Pol, May 04 2008

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (0,11,0,-10).

Crossrefs

Cf. A075427, A094025, A080610.

Programs

Magma

I:=[0,1,10,11]; [n le 4 select I[n] else 11*Self(n-2)-10*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Apr 25 2019

Mathematica

LinearRecurrence[{0, 11, 0, -10}, {0, 1, 10, 11}, 30] (* Vincenzo Librandi, Apr 25 2019 *)
CoefficientList[Series[x (1+10x)/((1-x^2)(1-10x^2)),{x,0,30}],x] (* Harvey P. Dale, Jul 07 2024 *)

Formula

a(n) = 10^(n/2)(5/9+sqrt(10)/18+(5/9-sqrt(10)/18)(-1)^n)-(-1)^n/2-11/18.