A218799 Number of solutions to x^2 + 2y^2 = n^2.

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

Links

Table of n, a(n) for n=0..87.

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

Cf. A218706, A218800.

Sequence in context: A320010 A210763 A281681 * A078770 A072038 A284315

Adjacent sequences: A218796 A218797 A218798 * A218800 A218801 A218802

Keyword

nonn

Author

Jon Perry, Nov 06 2012

Status

approved