[seqfan] Re: Conjecture: -6n+12 A603[n]+A605[n]-8 A604[n]-5 = 0

[Neil Sloane]

If you write that as an expression for A000605(n) in terms of the other
quantities, then it should follow by a simple counting argument

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Sun, Jan 4, 2015 at 9:06 AM, Georgi Guninski <guninski at guninski.com>
wrote:

> Numerical evidence suggests:
>
> -6n+12 A603[n]+A605[n]-8 A604[n]-5 = 0
>
> sage: uniq([-6*n+12*A603[n]+1*A605[n]-8*A604[n]-5 for n in [ 1 .. 499]])
> [0]
>
> A603 Number of nonnegative solutions to x^2 + y^2 <= n^2
> A604 Number of nonnegative solutions to x^2 + y^2 + z^2 <= n^2
> A605 Number of points of norm <= n in cubic lattice
>
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