cp's OEIS Frontend

A228108 Number of pairs (x, y) with 0 <= x, y <= n such that the distance between two points is a positive integer.

%I A228108 #27 Aug 15 2013 05:10:43
%S A228108 4,18,48,108,204,342,528,780,1100,1494,1968,2576,3292,4122,5104,6240,
%T A228108 7524,8962,10560,12348,14324,16494,18864,21600,24572,27786,31248,
%U A228108 34996,39012,43362,48000,52968,58244,63834,69840,76308,83132,90318,97872,105972,114468,123378,132704,142500,152892,163742,175056
%N A228108 Number of pairs (x, y) with 0 <= x, y <= n such that the distance between two points is a positive integer.
%C A228108 Pairs ((0, 1), (0, 0)) and ((0, 0), (0, 1)) are considered equal since they have the same points. ((0, 0), (0, 0)) isn't counted the distance between the points included isn't a positive integer. The x's and y's of points in a pair may differ due to Pythagoras, for example ((0, 0), (3, 4)).
%H A228108 David A. Corneth, <a href="/A228108/b228108.txt">Table of n, a(n) for n = 1..10560</a>
%H A228108 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean triple</a>
%o A228108 (PARI) a(n)=my(tot=n*(n+1)^2);forstep(i=1,sqrt(ceil(sqrt(n))^2)*(1+sqrt(2))\1,2,forstep(j=2,max(sqrt(ceil(sqrt(n+i^2))^2)\1,n\(2*i))*(1+sqrt(2))\1,2,if(gcd(i,j)==1,for(k=1,n\max(2*i*j,abs(j^2-i^2)),
%o A228108 tot+=(n-2*i*j*k+1)*(n-abs(j^2-i^2)*k+1)*4)))); tot \\_David A. Corneth_
%K A228108 nonn
%O A228108 1,1
%A A228108 _David A. Corneth_, Aug 10 2013