rms(1, ... , 2*k-1)

[Ignacio Larrosa Cañestro]

c.zizka at email.cz wrote:
> Dear Seqfans,
>
> Root Mean Square (1, 3, ... , 2*K-1) = C   (C,K positive integers)
>
> gives a nice Pell-like equation :
>
> 4*K*K - 3*C*C = 1
>
> Solutions :
> K = 1 , C = 1
> K = 13 , C = 15
> K = 181 , C = 209
>
> Are there other solutions ?

Yes,

K = 2521,  C = 2911
K = 35113,  C = 40545

This values of K, as like the values of C, verify the recurrence:

K(n) = 14K(n-1) - K(n-2)

The first ten solutions are:

K: [1, 13, 181, 2521, 35113, 489061, 6811741, 94875313, 1321442641, 
18405321661]

http://www.research.att.com/~njas/sequences/A001570

C: [1, 15, 209, 2911, 40545, 564719, 7865521, 109552575, 1525870529, 
21252634831]

http://www.research.att.com/~njas/sequences/A028230

Best regards,

Ignacio Larrosa Cañestro
A Coruña (España)
ilarrosa at mundo-r.com