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A218800 Number of nonnegative integer solutions to x^2 + 2y^2 = (3n)^2. 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 (list; graph; refs; listen; history; text; internal format)
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: A082204 A152727 A087159 * A062502 A141242 A130451

Adjacent sequences:  A218797 A218798 A218799 * A218801 A218802 A218803

KEYWORD

nonn

AUTHOR

Jon Perry, Nov 06 2012

STATUS

approved

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Last modified October 22 22:35 EDT 2021. Contains 348180 sequences. (Running on oeis4.)