A112713 Expansion of x/(1 - x + x^5 - x^6).

0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0

Offset: 0

Author

Paul Barry, Sep 15 2005

Keywords

• nonn
• easy

Comments

Decimal expansion of 10000/900009. - Elmo R. Oliveira, May 08 2024

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,-1,1).

Crossrefs

Cf. A000035, A133872, A088911, A131078, A112712.

Programs

Mathematica

CoefficientList[Series[x/(1 - x + x^5 - x^6), {x, 0, 100}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, -1, 1}, {0, 1, 1, 1, 1, 1}, 100] (* Harvey P. Dale, Feb 16 2014 *)

Formula

G.f.: x/(1 - x + x^5 - x^6) = x/((1-x)*(1+x)*(1-x+x^2-x^3+x^4)).

a(n) = a(n-1) - a(n-5) + a(n-6).

a(n) = a(n-10).

a(n) = (Sum_{k=0..floor((n+2)/2)} (-1)^(k+1)*C(n-k+2, k-1)*F(n-2*k+2)) mod 2.

a(n) = A112712(n) mod 2.

Extensions

Incorrect g.f. removed by Georg Fischer, May 15 2019