Problem

[Artur]

Dear Zak and Max,
Many, many thanks!
I was find expotential generating formula (inspite expected polynomial 
formula):
(1/2)((3/2-Sqrt[5]/2)^x-Sqrt[5](3/2-Sqrt[5]/2)^x+(3/2+Sqrt[5]/2)^x+Sqrt[5](3/2+Sqrt[5]/2)^x)

In Mathematica:
Table[Simplify[(1/2)((3/2-Sqrt[5]/2)^x-Sqrt[5](3/2-Sqrt[5]/2)^x+(3/2+Sqrt[5]/2)^x+Sqrt[5](3/2+Sqrt[5]/2)^x)],{x,0,50}]

ARTUR


zak seidov pisze:
> Artur: 
> a(n) = 3a(n - 1) - a(n - 2)
> Zak
>
> --- Artur <grafix at csl.pl> wrote:
>
>   
>> I'm apologize but but I was do mistake in formula
>> Find number m such that 5n^4(4+n^2) is square
>> Mathemtica sample Code:
>> a={};Do[If[IntegerQ[Sqrt[5n^4
>> (4+n^2)]],AppendTo[a,n]],{n,1,1364}];a
>>
>> Out: {1,4,11,29,76,199,521,1364}
>>
>> Artur pisze:
>>     
>>> Who have idea how solve folowing problem
>>>
>>> Find number m such that 5n^4(4+n)^2 is square
>>> or Sqrt[5] n^2(4+n) is integer
>>> a(n)= {1,4,11,29,76,199,...}
>>> I need ideas how find a(21) and more
>>>
>>> Artur
>>>
>>>
>>>       
>
>
>
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