

A160238


Numbers n such that n^2 can be expressed as the sum of three different nonzero Fibonacci numbers.


0



3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 17, 18, 20, 23, 24, 25, 32, 33, 35, 37, 40, 47, 57, 86, 112, 123, 139, 216, 322, 843, 1161, 1476, 2207, 3864, 4999, 5778, 15127, 39603, 103682, 271443, 710647, 1244196, 1860498, 4870847, 12752043
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OFFSET

1,1


COMMENTS

There exist a proper subsequence b(i)of a(n): n=[1, 2, 8, 17, 21, 24, 25, 28,29, 30, 31, 32, 33, 34, ...] such that approximatively b(i+1)=b(i)*(1+phi) where phi is 1.618... is the golden ratio and the approximation holds as a limit when i goes to infinity. For such a subsequence b(i) we have the following formula for the corresponding term when squared b(i)*b(i)=Fib(4*i+1)+Fib(4*i1)+Fib(3). In the previous example 4999=b(9).


LINKS

Table of n, a(n) for n=1..45.


EXAMPLE

4999*4999=24990001=Fib(37)+Fib(35)+Fib(3)


CROSSREFS

Cf. A000045, A135709, A135558.
Sequence in context: A261793 A262288 A236681 * A039165 A138220 A137913
Adjacent sequences: A160235 A160236 A160237 * A160239 A160240 A160241


KEYWORD

nonn


AUTHOR

Carmine Suriano, May 05 2009


EXTENSIONS

Inserted 4 (with 4^2=13+1+2), 6 (with 36=21+2+13), 12 (with 12^2=89+21+34) etc. Added "nonzero" to definition  R. J. Mathar, Oct 23 2010


STATUS

approved



