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.

1, 1, 1, 1, 9, 9, 9, 9, 21, 25, 25, 25, 37, 45, 49, 49, 69, 69, 77, 81, 101, 109, 117, 117, 141, 149, 157, 165, 189, 197, 205, 213, 241, 261, 269, 269, 305, 321, 333, 341, 377, 385, 401, 413, 449, 465, 481, 489, 529, 545

Offset: 1

Author

Nicholas Baeth, Sep 26 2016

Keywords

• nonn

Comments

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

References

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

Crossrefs

Cf. A000328.

Programs

Maple

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

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

Formula

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).