A077770 Number of ordered pairs of integers (x,y) with n^2 < x^2 + y^2 < (n+1)^2; number of lattice points between circles of radii n and n+1.

0, 4, 12, 16, 20, 28, 32, 44, 52, 52, 56, 60, 76, 80, 84, 84, 92, 104, 116, 116, 112, 140, 132, 136, 148, 148, 164, 160, 164, 180, 176, 204, 196, 204, 216, 196, 228, 216, 252, 236, 224, 260, 260, 284, 272, 260, 292, 288, 308, 300, 316, 312, 300, 332, 320, 364

Offset: 0

Author

T. D. Noe, Nov 20 2002

Keywords

• nonn

Comments

Note that 2*A077768(n)-a(n)/4 is the characteristic sequence for the Beatty sequence A001951(n).

Links

• Eric Weisstein's World of Mathematics, Gauss's Circle Problem

Crossrefs

Cf. A000328, A001951, A051132, A077768.

Programs

Mathematica

Table[Sum[SquaresR[2, k], {k, n^2 + 1, (n + 1)^2 - 1}], {n, 0, 100}]

Formula

a(n) = A051132(n+1) - A000328(n)