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
Keywords
Examples
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.
Programs
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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) -
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 *)
Comments