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A136483 Number of unit square lattice cells inside quadrant of origin-centered circle of diameter n. 4
0, 0, 1, 1, 3, 4, 6, 8, 13, 15, 19, 22, 28, 30, 37, 41, 48, 54, 64, 69, 77, 83, 94, 98, 110, 119, 131, 139, 152, 162, 172, 183, 199, 208, 226, 234, 253, 263, 281, 294, 308, 322, 343, 357, 377, 390, 412, 424, 447, 465, 488, 504, 528, 545, 567, 585, 612, 628, 654 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

As n -> infinity, lim a(n)/(n^2) -> Pi/16 (A019683).

LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum(floor(sqrt((n/2)^2 - k^2))), k = 1 ... floor(n/2).

a(n) = 1/4 * A136485(n) = 1/2 * A136513(n).

EXAMPLE

a(5) = 3 because a circle of radius 5/2 in the first quadrant encloses (2,1),(1,1),(1,2)

MATHEMATICA

Table[Sum[Floor[Sqrt[(n/2)^2 - k^2]], {k, 1, Floor[n/2]}], {n, 1, 100}]

CROSSREFS

Cf. Alternating merge of A136484 and A001182.

Sequence in context: A204658 A139041 A244607 * A240494 A280250 A004713

Adjacent sequences:  A136480 A136481 A136482 * A136484 A136485 A136486

KEYWORD

easy,nonn

AUTHOR

Glenn C. Foster (gfoster(AT)uiuc.edu), Jan 02 2008

STATUS

approved

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Last modified September 21 05:55 EDT 2020. Contains 337267 sequences. (Running on oeis4.)