A068785 Number of Cartesian lattice points in or on the circle x^2 + y^2 = 10^n.

5, 37, 317, 3149, 31417, 314197, 3141549, 31416025, 314159053, 3141592409, 31415925457, 314159264013, 3141592649625, 31415926532017, 314159265350589, 3141592653588533, 31415926535867961, 314159265358987341, 3141592653589764829, 31415926535897744669

Offset: 0

Author

Robert G. Wilson v, Mar 07 2002

Keywords

• nonn

Comments

a(n) ~ Pi*10^n [Shanks, page 164]. "Gauss gave [a(2)] = 317 and [a(4)] = 31417." [Shanks, page 165].

References

• Daniel Shanks, "Solved and Unsolved Problems in Number Theory," Fourth Edition, Chelsea Publishing Co., NY, 1993, pages 164-165 and 234 [gives a(n) for n = 8, 10, 12, 14].
• Wolfram Research, Mathematica 4, Standard Add-On Packages, Wolfram Media, Inc., Champaign, Il, 1999, pages 322-3.

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 0..36
• Index entries for sequences related to populations of quadratic forms

Crossrefs

Cf. A004018, A057961, A057655.

Programs

Mathematica

k = 1; s = 1; Do[s = s + SquaresR[2, n]; If[n == 10^k, k++; Print[s]], {n, 1, 10^6} ]

Formula

a(n) = Sum_{k=0..10^n} A004018(k). - Robert Israel, Jul 13 2014

Extensions

Definition and comments corrected by Jonathan Sondow, Dec 28 2012

a(0) corrected and a(9)-a(19) from Hiroaki Yamanouchi, Jul 13 2014