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A112713
Expansion of x/(1 - x + x^5 - x^6).
4
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
0,1
COMMENTS
Decimal expansion of 10000/900009. - Elmo R. Oliveira, May 08 2024
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.
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Sep 15 2005
EXTENSIONS
Incorrect g.f. removed by Georg Fischer, May 15 2019
STATUS
approved