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

[Ed Jeffery]

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?