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%I #7 Sep 15 2024 06:13:52
%S 0,1,8,41,183,770,3149,12730,51209,205356,822500,3292134,13172634,
%T 52698912,210812207,843281848,3373193506,13492906143,53971888157,
%U 215888078393,863553363881,3454215553470,13816866413106,55267474046659
%N Number of first quadrant lattice squares inside the circle x^2+y^2=(2^n)^2
%C a(n)/4^n converges to Pi/4 from below.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Gauss_circle_problem">Gauss circle problem</a> [From _Jaume Oliver Lafont_, Apr 20 2010]
%e Let + represent a square inside the circle and x a square traversed by the circle.
%e xx
%e +x a(1)=1
%e xxx
%e ++xx
%e +++x
%e +++x a(2)=8
%o (PARI) a(n)=sum(m=1,2^n-1,floor(sqrt(4^n-m^2)))
%Y Cf. A057655.
%Y Cf. A177144. [From _Jaume Oliver Lafont_, May 03 2010]
%K nonn
%O 0,3
%A _Jaume Oliver Lafont_, Feb 15 2009
%E a(19) corrected by Sophia Keith, Sep 15 2024