A218800 Number of nonnegative integer solutions to x^2 + 2y^2 = (3n)^2.

1, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 5, 3, 2, 2, 3, 2, 5, 4, 5, 2, 3, 5, 2, 3, 2, 2, 5, 2, 2, 3, 2, 2, 8, 5, 2, 4, 2, 5, 3, 2, 5, 3, 5, 5, 4, 2, 2, 3, 2, 2, 8, 2, 2, 5, 5, 2, 8, 2, 5, 3, 2, 2, 4, 2, 2, 8, 5, 5, 3, 2, 2, 4, 5, 2, 3, 5, 5, 3, 2, 2, 6, 5, 5, 3, 5, 5

Offset

0,2

Comments

For n > 0, a(n) > 1 since n^2 + 2(2n)^2 = (3n)^2 and (3n)^2 + 2*0^2 = (3n)^2.

a(3k) > 2 as we also have (7k)^2 + 2*(4k)^2 = 81k^2 =

(9k)^2 = (3*3k)^2.

Links

Table of n, a(n) for n=0..86.

Example

a(2) = 2 because we have 6^2 + 2*0^2 = 6^2 and 2^2 + 2*4^2 = 6^2 and no others.

Prog

(JavaScript)
for (i=0; i<200; i+=3) {
d=0; e=0;
for (a=0; a<=i; a++)
for (b=0; b<=i; b++) {
t1=Math.pow(a, 2)+2*Math.pow(b, 2);
t2=Math.pow(i, 2);
if (t1<t2) d++;
if (t1<=t2) e++;
}
document.write((e-d)+", ");
}

Crossrefs

Cf. A218799.

Sequence in context: A152727 A087159 A366922 * A062502 A141242 A130451

Adjacent sequences: A218797 A218798 A218799 * A218801 A218802 A218803

Keyword

nonn

Author

Jon Perry, Nov 06 2012

Status

approved