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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

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.

LINKS

Table of n, a(n) for n=1..50.

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).

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

PROG

(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

CROSSREFS

Cf. A000328.

Sequence in context: A068395 A245429 A242893 * A293832 A277223 A144586

Adjacent sequences:  A275482 A275483 A275484 * A275486 A275487 A275488

KEYWORD

nonn

AUTHOR

Nicholas Baeth, Sep 26 2016

STATUS

approved

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Last modified May 23 12:38 EDT 2019. Contains 323514 sequences. (Running on oeis4.)