A077768 Number of times that the sum of two squares is an integer between n^2 and (n+1)^2; multiple representations are counted multiply.

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, 20, 21, 23, 22, 26, 25, 26, 27, 25, 29, 27, 32, 30, 28, 33, 33, 36, 34, 33, 37, 36, 39, 38, 40, 39, 38, 42, 40, 46, 43, 45, 44, 46, 48, 47, 49, 50, 48, 50, 50, 53, 55, 52, 55, 53, 60, 57

Offset: 1

Author

T. D. Noe, Nov 20 2002

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

Cf. A001951, A077769, A077770.

Programs

Mathematica

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