A077768 - OEIS

%I #4 Mar 30 2012 17:22:26

%S 1,2,2,3,4,4,6,7,7,7,8,10,10,11,11,12,13,15,15,14,18,17,17,19,19,21,

%T 20,21,23,22,26,25,26,27,25,29,27,32,30,28,33,33,36,34,33,37,36,39,38,

%U 40,39,38,42,40,46,43,45,44,46,48,47,49,50,48,50,50,53,55,52,55,53,60,57

%N Number of times that the sum of two squares is an integer between n^2 and (n+1)^2; multiple representations are counted multiply.

%C Related to the circle problem, cf. A077770. Note that 2*a(n)-A077770(n)/4 is the characteristic sequence for the Beatty sequence A001951. See A077769 for a more restrictive case. A077773 counts multiple representations only once.

%e a(8)=7 because 65=64+1, 65=49+16, 68=64+4, 72=36+36, 73=64+9, 74=49+25 and 80=64+16 are between squares 64 and 81. Note that 65 occurs twice.

%t maxN=100; lst={}; For[n=1, n<=maxN, n++, cnt=0; 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, cnt++ ]; j++ ]; i--; j-- ]; AppendTo[lst, cnt]]; lst

%Y Cf. A001951, A077769, A077770.

%K nonn

%O 1,2

%A _T. D. Noe_, Nov 20 2002