A094027 Expansion of x(1+100x)/((1-x^2)(1-100x^2)).

0, 1, 100, 101, 10100, 10101, 1010100, 1010101, 101010100, 101010101, 10101010100, 10101010101, 1010101010100, 1010101010101, 101010101010100, 101010101010101, 10101010101010100, 10101010101010101

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))

Links

• Index entries for linear recurrences with constant coefficients, signature (0,101,0,-100).

Crossrefs

Cf. A075427, A094025, A080610 (interpreted as binary), A094026.

Formula

a(n)=2^n*5^(n+1)((-1)^n/11+1/9)-(-1)^n/2-101/198