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A102460
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a(n) = 1 if n is a Lucas number, else a(n) = 0.
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5
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0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The number of nonnegative integer solutions to 25*x^4-10*n^2*x^2+n^4-16=0. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
a(n)=1 if and only if there is an integer m such that x=n is a root of p(x)=x^4-10*m^2*x^2+25*m^4-16. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
For n>=3: a(n)=1 iff floor(log_phi(n+1/2))=ceiling(log_phi(n-1/2)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
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LINKS
| Index entries for characteristic functions
Casey Mongoven, Lucas Binary no. 1; electronic music created with this sequence.
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FORMULA
| G.f.: g(x)=sum{k>=0, x^A000032(k)}. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
a(n)=1+floor(arsinh(n/2)/ln(phi))-ceiling(arcosh(n/2)/ln(phi)) for n>=3, where phi=(1+sqr(5))/2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
a(n)=1+A130241(n)-A130242(n) for n>=3. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
a(n)=1+A130247(n)-A130242(n) for n=>2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
a(n)=A130245(n)-A130245(n-1) for n>=1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
For n>=3: a(n)=1 iff A130241(n)=A130242(n). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 02 2007
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CROSSREFS
| Cf. A000032, A010056.
Cf. partial sums A130245. Also A130241, A130242, A130247, A104162, A105348, A000032.
Sequence in context: A138886 A099859 A176416 * A080908 A131720 A131719
Adjacent sequences: A102457 A102458 A102459 * A102461 A102462 A102463
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KEYWORD
| nonn
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AUTHOR
| Casey Mongoven (cm(AT)caseymongoven.com), Apr 18 2005
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