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 A077774 #7 Sep 18 2013 14:20:36
%S A077774 0,1,1,1,1,2,2,2,3,3,2,3,4,3,3,5,4,4,5,5,5,5,6,5,5,7,6,6,6,8,7,7,8,9,
%T A077774 8,7,8,9,7,9,10,7,11,10,9,10,13,11,8,11,12,12,11,11,13,11,13,12,12,13,
%U A077774 13,13,14,14,13,14,13,15,13,15,14,17,15,14,17,16,16,16,17,16,18,18,16,15
%N A077774 Number of integers between n^2 and (n+1)^2 that are the sum of two coprime squares of opposite parity; multiple representations are counted once.
%C A077774 See A077773 for a similar, but less restrictive sequence. A077769 counts multiple representations multiply.
%H A077774 T. D. Noe, <a href="/A077774/b077774.txt">Table of n, a(n) for n = 1..1000</a>
%e A077774 a(8)=2 because 65=64+1=49+16 and 73=64+9 are between squares 49 and 64. Note that 65 is counted only once.
%t A077774 maxN=100; lst={}; For[n=1, n<=maxN, n++, sqrs={}; i=n; j=0; While[i>=j, j=1; While[i^2+j^2<(n+1)^2, If[i>=j&&i^2+j^2>n^2&&GCD[i, j]==1&&OddQ[i]==EvenQ[j], AppendTo[sqrs, i^2+j^2]]; j++ ]; i--; j-- ]; AppendTo[lst, Length[Union[sqrs]]]]; lst
%Y A077774 Cf. A077769, A077773.
%K A077774 nonn
%O A077774 1,6
%A A077774 _T. D. Noe_, Nov 20 2002