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

0,3

Comments

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

Links

Table of n, a(n) for n=0..23.

Wikipedia, Gauss circle problem [From Jaume Oliver Lafont, Apr 20 2010]

Example

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

Prog

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

Crossrefs

Cf. A057655.

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

Sequence in context: A273112 A272925 A272944 * A272996 A273070 A273145

Adjacent sequences: A156787 A156788 A156789 * A156791 A156792 A156793

Keyword

nonn

Author

Jaume Oliver Lafont, Feb 15 2009

Extensions

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

Status

approved