A156790 Number of first quadrant lattice squares inside the circle x^2+y^2=(2^n)^2.

0, 1, 8, 41, 183, 770, 3149, 12730, 51209, 205356, 822500, 3292134, 13172634, 52698912, 210812207, 843281848, 3373193506, 13492906143, 53971888157, 215888078393, 863553363881, 3454215553470, 13816866413106, 55267474046659

Offset: 0

Author

Jaume Oliver Lafont, Feb 15 2009

Keywords

• nonn

Comments

a(n)/4^n converges to Pi/4 from below.

Examples

			Let + represent a square inside the circle and x a square traversed by the circle.
xx
+x a(1)=1
xxx
++xx
+++x
+++x a(2)=8
		

Links

• Wikipedia, Gauss circle problem [From _Jaume Oliver Lafont_, Apr 20 2010]

Crossrefs

Cf. A057655.

Cf. A177144. [From Jaume Oliver Lafont, May 03 2010]

Programs

PARI

a(n)=sum(m=1,2^n-1,floor(sqrt(4^n-m^2)))

Extensions

a(19) corrected by Sophia Keith, Sep 15 2024