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%I #23 Jun 22 2022 02:33:51
%S 1,2,1,1,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%T 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N Indicator sequence for the Fibonacci numbers.
%C Without multiplicities, this is A010056.
%C The number of nonnegative integer solutions of x^4 - 10*n^2*x^2 + 25*n^4 - 16 = 0. - _Hieronymus Fischer_, May 17 2007
%F G.f.: Sum{k>=0} x^F(k).
%F From _Hieronymus Fischer_, May 17 2007: (Start)
%F a(n) = 1+floor(arcsinh(sqrt(5)*n/2)/log(phi))-ceiling(arccosh(sqrt(5)*n/2)/log(phi)), for n>0, where phi=(1+sqrt(5))/2.
%F a(n) = A108852(n) - A108852(n-1) for n>0.
%F a(n) = A130233(n) - A130233(n-1) for n>0.
%F a(n) = 1 + A130233(n) - A130234(n) for n>0.
%F a(n) = A130234(n+1) - A130234(n) for n>=0. (End)
%e a(1)=2 since F(1)=F(2)=1.
%o (PARI) a(n)=if(n==1,return(2)); my(k=n^2);k+=((k + 1) << 2);issquare(k) || issquare(k-8) \\ _Charles R Greathouse IV_, Feb 03 2014; typo corrected by _Georg Fischer_, Jun 22 2022
%Y Cf. A000045.
%Y Partial sums are in A108852. See also A130233 and A130234.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Apr 01 2005
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