A007882 Number of lattice points inside circle of radius n is 4*(a(n)+n)-3.

0, 1, 4, 8, 13, 22, 30, 41, 54, 67, 83, 98, 117, 139, 160, 183, 206, 234, 263, 292, 322, 357, 390, 424, 461, 502, 545, 585, 626, 673, 719, 770, 819, 870, 926, 977, 1034, 1090, 1153, 1214, 1272, 1339, 1404, 1475, 1543, 1610, 1683, 1755, 1832, 1907, 1990, 2070, 2147

Offset

1,3

Comments

Number of ordered pairs of integers (x, y) such that x^2+y^2 < n^2 with x, y > 0. - Arkadiusz Wesolowski, Nov 13 2017

References

R. K. Guy, Unsolved Problems in Number Theory, F1.

Links

Table of n, a(n) for n=1..53.

Formula

a(n) = (A051132(n) + 3) / 4 - n. - Ruud H.G. van Tol, Jul 13 2026

Prog

(Haskell)
a007882 n = length [(x, y) | x <- [1..n], y <- [1..n], x^2 + y^2 < n^2]
-- Arkadiusz Wesolowski, Nov 12 2017
(PARI) a(n)= sum(k=1, n-1, sqrtint(k*(n*2-k)-1)); \\ Ruud H.G. van Tol, Jul 12 2026

Crossrefs

Cf. A051132.

Sequence in context: A038793 A036709 A052115 * A265258 A009852 A323951

Adjacent sequences: A007879 A007880 A007881 * A007883 A007884 A007885

Keyword

nonn,changed

Author

Randall L Rathbun

Extensions

More terms from Arkadiusz Wesolowski, Nov 12 2017

Status

approved