cp's OEIS Frontend

A275485 Number of integer lattice points from an n X n square in R^2 centered at the origin that are closer (measured using the Euclidean metric) to the origin than to any of the four sides of the square.

%I A275485 #31 Sep 29 2016 02:43:50
%S A275485 1,1,1,1,9,9,9,9,21,25,25,25,37,45,49,49,69,69,77,81,101,109,117,117,
%T A275485 141,149,157,165,189,197,205,213,241,261,269,269,305,321,333,341,377,
%U A275485 385,401,413,449,465,481,489,529,545
%N A275485 Number of integer lattice points from an n X n square in R^2 centered at the origin that are closer (measured using the Euclidean metric) to the origin than to any of the four sides of the square.
%C A275485 There is a formula, but no closed form, for computing the entries of the sequence.
%D A275485 N. R. Baeth, L. Luther and R. McKee, Variations on a Putnam Problem, preprint, 2016.
%F A275485 a(n) = (2*floor(n*(sqrt(2)-1)/2)+1)^2+4*Sum_{i=ceiling(-n*(sqrt(2)-1)/2)..floor(n*(sqrt(2)-1)/2)} ceiling(n/4-i^2/n)-1-floor(n*(sqrt(2)-1)/2).
%p A275485 A275485:=n->(2*floor(n*(sqrt(2)-1)/2)+1)^2+4*add(ceil(n/4-i^2/n)-1-floor(n*(sqrt(2)-1)/2), i=ceil(-n*(sqrt(2)-1)/2)..floor(n*(sqrt(2)-1)/2)): seq(A275485(n), n=1..100); # _Wesley Ivan Hurt_, Sep 27 2016
%o A275485 (PARI) a(n)=(2*floor(n*(sqrt(2)-1)/2)+1)^2+4*sum(i=ceil(-n*(sqrt(2)-1)/2),floor(n*(sqrt(2)-1)/2), ceil(n/4-i^2/n)-1-floor(n*(sqrt(2)-1)/2)); \\ _Joerg Arndt_, Sep 27 2016
%Y A275485 Cf. A000328.
%K A275485 nonn
%O A275485 1,5
%A A275485 _Nicholas Baeth_, Sep 26 2016