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%I #7 Sep 18 2013 14:20:36
%S 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 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 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 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 See A077773 for a similar, but less restrictive sequence. A077769 counts multiple representations multiply.
%H T. D. Noe, <a href="/A077774/b077774.txt">Table of n, a(n) for n = 1..1000</a>
%e 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 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 Cf. A077769, A077773.
%K nonn
%O 1,6
%A _T. D. Noe_, Nov 20 2002
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