login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2

%I #31 Sep 29 2016 02:43:50

%S 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 141,149,157,165,189,197,205,213,241,261,269,269,305,321,333,341,377,

%U 385,401,413,449,465,481,489,529,545

%N 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 There is a formula, but no closed form, for computing the entries of the sequence.

%D N. R. Baeth, L. Luther and R. McKee, Variations on a Putnam Problem, preprint, 2016.

%F 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:=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 (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 Cf. A000328.

%K nonn

%O 1,5

%A _Nicholas Baeth_, Sep 26 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)