What next in 0,1,6,25,96,361,1350,5041?
Henry in Rotherhithe
se16 at btinternet.com
Sun Mar 14 02:54:27 CET 2004
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There are also the repeating
S_1 = A011655 (0,1,1,0,1,1,...)
S_2 = A007877 (0,1,2,1,0,1,2,1,...)
S_3 = A078070(unsigned) (0,1,3,4,3,1,0,1,3,4,3,1,...)
> -----Original Message-----
> From: r.rosenthal at web.de
> Sent: 13 March 2004 22:46
> To: seqfan at ext.jussieu.fr
> Subject: What next in 0,1,6,25,96,361,1350,5041?
>
>
> Another way of putting the question above:
>
> What have the following sequences in common:
>
> S_4 = A000290 the squares
> S_5 = A004146 Alternate Lucas Numbers - 2
> S_7 = A054493 A Pellian-related sequence
> S_8 = A001108 a(n)-th triangular number is a square
> S_9 = A049684 F(2n)^2 where F() = Fibonacci numbers
> S_20 = A049683 a(n)=(L(6n)-2)/16, L=Lucas Sequence
> S_25 = A089927* Expansion of 1/((1-x^2)(1-5x+x^2))
> S_36 = A001110 Both triangular and square
> S_49 = A049682 a(n)=(L(8n)-2)/45, L=Lucas sequence
> S_144 = A004191^2 a(n)=S(n,12) (Chebyshev's poly 2. kind)
>
> where A089927*(n) = A089927(2n-2)
>
>
> Answer: for any three successive members a, b, c we have
> a * c = (b-1)^2, i.e. the obey the recurrence
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> a(n-1) * a(n+1) = ( a(n) - 1 )^2
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
>
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