[seqfan] Re: A147296

[Maximilian Hasler]

Indeed  A147296(n) is by definition the numerator of

[ (9n+1)²-1 ] / [ 9 (9n+1)² ]
= [ 81n² + 18n ] / [ 9(9n+1)² ]
= [ 9n² + 2n ] / (9n+1)²
= n ( 9n + 2 ) / (9n+1)²

and gcd ( n, 9n+1 ) = gcd(9n+2, 9n+1 ) = 1

so  A147296(n) =  n ( 9n + 2 )
as conjectured.

Maximilian

On Sun, Mar 1, 2009 at 3:03 AM, vincenzo.librandi at tin.it
<vincenzo.librandi at tin.it> wrote:
> Comment:
>
> I believe the formula is
>
> a(n)=n(9n+2)
>
> (0, 11, 40, 87, 152,
> 235, 336, 455, 592, 747, 920, 1111, 1320, 1547, 1792, 2055, 2336,
> 2635, 2952, 3287, 3640,  4011, 4400, 4807, 5232, 5675, 6136, 6615,
> 7112, 7627, 8160, 8711, 9280, 9867, 10472, 11095, 11736, 12395, 13072,
> 13767, 14480, 15211, 15960, 16727, 17512, 18315,...,)
>
> Regards,
> Vincenzo Librandi
>
>
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