login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A218799
Number of solutions to x^2 + 2y^2 = n^2.
4
1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 2, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 5, 2, 1, 3, 1, 2, 2, 1, 2, 2, 2, 2, 3, 1, 1, 2, 1, 1, 5, 1, 1, 4, 2, 1, 5, 1, 2, 2, 1, 1, 3, 1, 1, 5, 2, 2, 2, 1, 1, 3, 2, 1, 2, 2, 2, 2, 1, 1, 5, 2, 2, 2, 2, 2, 2
OFFSET
0,4
COMMENTS
a(3k) > 1 for all k > 0 because k^2 + 2(2k)^2 = (3k)^2.
Terms with index n^2 in A216282. - Joerg Arndt, Nov 06 2012
EXAMPLE
a(9) = 3 because we have 9^2 + 2*0^2 = 9^2, 3^2 + 2*6^2 = 9^2 and 7^2 + 2*4^2 = 9^2 and no others.
MATHEMATICA
nn = 87; t = Sort[Select[Flatten[Table[x^2 + 2*y^2, {x, 0, nn}, {y, 0, nn}]], # <= nn^2 &]]; Table[Count[t, _?(# == n^2 &)], {n, 0, nn}] (* T. D. Noe, Nov 06 2012 *)
PROG
(JavaScript)
for (i=0; i<100; i++) {
d=0; e=0;
for (a=0; a<=i; a++)
for (b=0; b<=i; b++) {
if (Math.pow(a, 2)+2*Math.pow(b, 2)<Math.pow(i, 2)) d++;
if (Math.pow(a, 2)+2*Math.pow(b, 2)<=Math.pow(i, 2)) e++;
}
document.write((e-d)+", ");
}
CROSSREFS
Sequence in context: A320010 A210763 A281681 * A078770 A072038 A284315
KEYWORD
nonn
AUTHOR
Jon Perry, Nov 06 2012
STATUS
approved