Search: id:A104162
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%I A104162
%S A104162 1,2,1,1,0,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,
%T A104162 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A104162 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A104162 Indicator sequence for the Fibonacci numbers.
%C A104162 Without multiplicities, this is A010056.
%C A104162 The number of nonnegative integer solutions of x^4-10*n^2*x^2+25*n^4-16=0. 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007
%F A104162 G.f. : sum{k>=0, x^F(k)}
%F A104162 a(n)=1+floor(arsinh(sqr(5)*n/2)/ln(phi))-ceiling(arcosh(sqr(5)*n/2)/ln(phi)), 
               for n>0, where phi=(1+sqr(5))/2. Also true: a(n)=A108852(n)-A108852(n-1)=A130233(n)-A130233(n-1)=1+A13023\
               3(n)-A130234(n) for n>0 and a(n)=A130234(n+1)-A130234(n) for n>=0. 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 17 2007
%e A104162 a(1)=2 since F(1)=F(2)=1.
%Y A104162 Cf. A000045.
%Y A104162 Partial sums are in A108852. See also A130233 and A130234.
%Y A104162 Sequence in context: A160381 A089311 A086784 this_sequence A145679 A007273 
               A016319
%Y A104162 Adjacent sequences: A104159 A104160 A104161 this_sequence A104163 A104164 
               A104165
%K A104162 easy,nonn
%O A104162 0,2
%A A104162 Paul Barry (pbarry(AT)wit.ie), Apr 01 2005

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