This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A218800 #18 Nov 07 2012 13:46:36 %S A218800 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, %T A218800 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, %U A218800 5,3,2,2,4,5,2,3,5,5,3,2,2,6,5,5,3,5,5 %N A218800 Number of nonnegative integer solutions to x^2 + 2y^2 = (3n)^2. %C A218800 For n > 0, a(n) > 1 since n^2 + 2(2n)^2 = (3n)^2 and (3n)^2 + 2*0^2 = (3n)^2. %C A218800 a(3k) > 2 as we also have (7k)^2 + 2*(4k)^2 = 81k^2 = %C A218800 (9k)^2 = (3*3k)^2. %e A218800 a(2) = 2 because we have 6^2 + 2*0^2 = 6^2 and 2^2 + 2*4^2 = 6^2 and no others. %o A218800 (JavaScript) %o A218800 for (i=0; i<200; i+=3) { %o A218800 d=0; e=0; %o A218800 for (a=0; a<=i; a++) %o A218800 for (b=0; b<=i; b++) { %o A218800 t1=Math.pow(a, 2)+2*Math.pow(b, 2); %o A218800 t2=Math.pow(i, 2); %o A218800 if (t1<t2) d++; %o A218800 if (t1<=t2) e++; %o A218800 } %o A218800 document.write((e-d)+", "); %o A218800 } %Y A218800 Cf. A218799. %K A218800 nonn %O A218800 0,2 %A A218800 _Jon Perry_, Nov 06 2012