[seqfan] Re: A000021: Number of positive integers <= 2^n of form x^2 + 12 y^2.

Neil Sloane njasloane at gmail.com
Sat Apr 14 19:06:57 CEST 2012

Ed, it doesn't matter HOW we get get the number, just
whether or not we get it.

Color a number blue if it is of the form x^2+12y^2.
a(n) = number of blue numbers <= 2^n

Neil

On Sat, Apr 14, 2012 at 12:50 PM, Ed Jeffery <lejeffery7 at gmail.com> wrote:

> Hello,
>
> A000021 = {1, 1, 2, 2, 6, 9, 17, 30, 54} (offset 0,3).
>
> For this sequence, are we counting representations (or partitions)? If so,
> then the example for n = 4 is
>
> "EXAMPLE      a(4)=6 since 2^4=16 and 1=1^2, 4=2^2, 9=3^2, 12=12*1^2,
> 13=1^2+12*1^2, 16=4^2,"
>
>
> but we also have
>
> 16 = 2^2 + 12*1^2,
>
> with the set of distinct pairs then being
>
> {(1,0), (2,0), (3,0), (0,1), (1,1), (2,1), (4,0)}
>
> of order 7. So I have to ask:
>
> Should a(4) = 7?
>
> Are the other terms of this sequence correct?
>
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--
Dear Friends, I will soon be retiring from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA